I will make you as a light for the nations, that my salvation may reach to the end of the earth.

Psalm 22:26 The meek shall eat and be satisfied: they shall praise the LORD that seek him: your heart shall live for ever. 27 All the ends of the world shall remember and turn unto the LORD: and all the families of the nations shall worship before you. 28 For the kingdom is the LORD'S: and he is the governor among the nations.

Isaiah 60: 3 And nations shall come to your light, and kings to the brightness of your rising. 4 Lift up your eyes all around, and see; they all gather together, they come to you; your sons shall come from afar, and your daughters shall be carried on the hip. 5 Then you shall see and be radiant; your heart shall thrill and exult, because the abundance of the sea shall be turned to you, the wealth of the nations shall come to you. (ESV)

Isaiah 49:6 He says: “It is too light a thing that you should be my servant to raise up the tribes of Jacob and to bring back the preserved of Israel; I will make you as a light for the nations, that my salvation may reach to the end of the earth.”...8 Thus said the LORD, In an acceptable time have I heard you, and in a day of salvation have I helped you: and I will preserve you, and give you for a covenant of the people, to establish the earth, to cause to inherit the desolate heritages;

Isaiah 11:10 And in that day there shall be a root of Jesse, which shall stand for an ensign of the people; to it shall the Gentiles seek: and his rest shall be glorious.

Isaiah 52:7 How beautiful on the mountains are the feet of him that brings good tidings, that publishes peace; that brings good tidings of good, that publishes salvation; that said to Zion, Your God reigns! ..... 10 The LORD has made bare his holy arm in the eyes of all the nations; and all the ends of the earth shall see the salvation of our God.... 13 Behold, my servant (the messiah) shall deal prudently, he shall be exalted and extolled, and be very high. 14 As many were astonished at you; his visage was so marred more than any man, and his form more than the sons of men: 15 So shall he sprinkle many nations; the kings shall shut their mouths at him: for that which had not been told them shall they see; and that which they had not heard shall they consider.

Isaiah 42:Behold my servant, (the messiah) whom I uphold; my elect, in whom my soul delights; I have put my spirit on him: he shall bring forth judgment to the Gentiles. 2 He shall not cry, nor lift up, nor cause his voice to be heard in the street. 3 A bruised reed shall he not break, and the smoking flax shall he not quench: he shall bring forth judgment to truth. 4 He shall not fail nor be discouraged, till he have set judgment in the earth: and the isles shall wait for his law. 5 Thus said God the LORD, he that created the heavens, and stretched them out; he that spread forth the earth, and that which comes out of it; he that gives breath to the people on it, and spirit to them that walk therein: 6 I the LORD have called you in righteousness, and will hold your hand, and will keep you, and give you for a covenant of the people, for a light of the Gentiles; 7 To open the blind eyes, to bring out the prisoners from the prison, and them that sit in darkness out of the prison house.

Psalm 72:2 He shall judge your people with righteousness, and your poor with judgment. 3 The mountains shall bring peace to the people, and the little hills, by righteousness. 4 He shall judge the poor of the people, he shall save the children of the needy, and shall break in pieces the oppressor. 5 They shall fear you as long as the sun and moon endure, throughout all generations. 6 He shall come down like rain on the mown grass: as showers that water the earth. 7 In his days shall the righteous flourish; and abundance of peace so long as the moon endures. 8 He shall have dominion also from sea to sea, and from the river to the ends of the earth. 9 They that dwell in the wilderness shall bow before him; and his enemies shall lick the dust. 10 The kings of Tarshish and of the isles shall bring presents: the kings of Sheba and Seba shall offer gifts. 11 Yes, all kings shall fall down before him: all nations shall serve him. 12 For he shall deliver the needy when he cries; the poor also, and him that has no helper. 13 He shall spare the poor and needy, and shall save the souls of the needy. 14 He shall redeem their soul from deceit and violence: and precious shall their blood be in his sight. 15 And he shall live, and to him shall be given of the gold of Sheba: prayer also shall be made for him continually; and daily shall he be praised. 16 There shall be an handful of corn in the earth on the top of the mountains; the fruit thereof shall shake like Lebanon: and they of the city shall flourish like grass of the earth. 17 His name shall endure for ever: his name shall be continued as long as the sun: and men shall be blessed in him: all nations shall call him blessed. 18 Blessed be the LORD God, the God of Israel, who only does wondrous things. 19 And blessed be his glorious name for ever: and let the whole earth be filled with his glory; Amen, and Amen.

Psalm 67: 1 God be merciful to us, and bless us; and cause his face to shine on us; Selah. 2 That your way may be known on earth, your saving health among all nations. 3 Let the people praise you, O God; let all the people praise you. 4 O let the nations be glad and sing for joy: for you shall judge the people righteously, and govern the nations on earth. Selah. 5 Let the people praise you, O God; let all the people praise you. 6 Then shall the earth yield her increase; and God, even our own God, shall bless us. 7 God shall bless us; and all the ends of the earth shall fear him.

Psalm 82: 8 Arise, O God, judge the earth: for you shall inherit all nations.

Psalm 86: 9 All nations whom you have made shall come and worship before you, O Lord; and shall glorify your name.

Isaiah 2:2 And it shall come to pass in the last days, that the mountain of the LORD's house shall be established in the top of the mountains, and shall be exalted above the hills; and all nations shall flow to it. 3 And many people shall go and say, Come you, and let us go up to the mountain of the LORD, to the house of the God of Jacob; and he will teach us of his ways, and we will walk in his paths: for out of Zion shall go forth the law, and the word of the LORD from Jerusalem. 4 And he shall judge among the nations, and shall rebuke many people: and they shall beat their swords into plowshares, and their spears into pruning hooks: nation shall not lift up sword against nation, neither shall they learn war any more. Please see a very concise New Testament interpretation of the illustrations used in Isaiah 2's wording

Isaiah 54 and 55 are directly speaking about the new Jerusalem.

Isaiah 54:1 Sing, O barren, you that did not bear; break forth into singing, and cry aloud, you that did not travail with child: for more are the children of the desolate than the children of the married wife, said the LORD. 2 Enlarge the place of your tent, and let them stretch forth the curtains of your habitations: spare not, lengthen your cords, and strengthen your stakes; 3 For you shall break forth on the right hand and on the left; and your descendants shall inherit the Gentiles, and make the desolate cities to be inhabited. 4 Fear not; for you shall not be ashamed: neither be you confounded; for you shall not be put to shame: for you shall forget the shame of your youth, and shall not remember the reproach of your widowhood any more. 5 For your Maker is your husband; the LORD of hosts is his name; and your Redeemer the Holy One of Israel; The God of the whole earth shall he be called.

Isaiah 55:3....I will make an everlasting covenant with you, even the sure mercies of David. 4 Behold, I have given him for a witness to the people, a leader and commander to the people. 5 Behold, you shall call a nation that you know not, and nations that knew not you shall run to you because of the LORD your God, and for the Holy One of Israel; for he has glorified you. .....10 For as the rain comes down, and the snow from heaven, and returns not thither, but waters the earth, and makes it bring forth and bud, that it may give seed to the sower, and bread to the eater: 11 So shall my word be that goes forth out of my mouth: it shall not return to me void, but it shall accomplish that which I please, and it shall prosper in the thing whereto I sent it. 12 For you shall go out with joy, and be led forth with peace: the mountains and the hills shall break forth before you into singing, and all the trees of the field shall clap their hands. (The mountains and trees are typical Biblical illustrations of the nations.)13 Instead of the thorn shall come up the fir tree, and instead of the brier shall come up the myrtle tree: and it shall be to the LORD for a name, for an everlasting sign that shall not be cut off.

Isaiah 49:1 Listen, O isles, to me; and listen, you people, from far; The LORD has called me from the womb; from the bowels of my mother has he made mention of my name. 2 And he has made my mouth like a sharp sword; in the shadow of his hand has he hid me, and made me a polished shaft; in his quiver has he hid me;..... 6 And he said, It is a light thing that you should be my servant to raise up the tribes of Jacob, and to restore the preserved of Israel: I will also give you for a light to the Gentiles, that you may be my salvation to the end of the earth. 7 Thus said the LORD, the Redeemer of Israel, and his Holy One, to him whom man despises, to him whom the nation abhors, to a servant of rulers, Kings shall see and arise, princes also shall worship, because of the LORD that is faithful, and the Holy One of Israel, and he shall choose you. 8 Thus said the LORD, In an acceptable time have I heard you, and in a day of salvation have I helped you: and I will preserve you, and give you for a covenant of the people, to establish the earth, to cause to inherit the desolate heritages; 9 That you may say to the prisoners, Go forth; to them that are in darkness, Show yourselves. They shall feed in the ways, and their pastures shall be in all high places. 10 They shall not hunger nor thirst; neither shall the heat nor sun smite them: for he that has mercy on them shall lead them, even by the springs of water shall he guide them. 11 And I will make all my mountains a way, and my highways shall be exalted. 12 Behold, these shall come from far: and, see, these from the north and from the west; and these from the land of Sinim. 13 Sing, O heavens; and be joyful, O earth; and break forth into singing, O mountains: for the LORD has comforted his people, and will have mercy on his afflicted. 14 But Zion said, The LORD has forsaken me, and my Lord has forgotten me. 15 Can a woman forget her sucking child, that she should not have compassion on the son of her womb? yes, they may forget, yet will I not forget you. 16 Behold, I have graven you on the palms of my hands; your walls are continually before me. 17 Your children shall make haste; your destroyers and they that made you waste shall go forth of you. 18 Lift up your eyes round about, and behold: all these gather themselves together, and come to you. As I live, said the LORD, you shall surely clothe you with them all, as with an ornament, and bind them on you, as a bride does. 19 For your waste and your desolate places, and the land of your destruction, shall even now be too narrow by reason of the inhabitants, and they that swallowed you up shall be far away. 20 The children which you shall have, after you have lost the other, shall say again in your ears, The place is too strait for me: give place to me that I may dwell. 21 Then shall you say in your heart, Who has begotten me these, seeing I have lost my children, and am desolate, a captive, and removing to and fro? and who has brought up these? Behold, I was left alone; these, where had they been? 22 Thus said the Lord GOD, Behold, I will lift up my hand to the Gentiles, and set up my standard to the people: and they shall bring your sons in their arms, and your daughters shall be carried on their shoulders. 23 And kings shall be your nursing fathers, and their queens your nursing mothers: they shall bow down to you with their face toward the earth, and lick up the dust of your feet; and you shall know that I am the LORD: for they shall not be ashamed that wait for me. 24 Shall the prey be taken from the mighty, or the lawful captive delivered? 25 But thus said the LORD, Even the captives of the mighty shall be taken away, and the prey of the terrible shall be delivered: for I will contend with him that contends with you, and I will save your children. 26 And I will feed them that oppress you with their own flesh; and they shall be drunken with their own blood, as with sweet wine: and all flesh shall know that I the LORD am your Savior and your Redeemer, the mighty One of Jacob.

Isaiah 56:6 Also the sons of the stranger, (gentiles) that join themselves to the LORD, to serve him, and to love the name of the LORD, to be his servants, every one that keeps the Sabbath from polluting it, and takes hold of my covenant; (The New Covenant) 7 Even them will I bring to my holy mountain, and make them joyful in my house of prayer: their burnt offerings and their sacrifices shall be accepted on my altar; for my house shall be called an house of prayer for all people. (The house and temple of the Lord is his people.) 8 The Lord GOD, which gathers the outcasts of Israel said, Yet will I gather others to him, beside those that are gathered to him.

The first part of Isaiah 61 is one of those widely known scriptures in the Bible because Jesus quoted it in the NT as speaking of himself. The OT rendition however also shows the eventual effects of Christ's ministry in the earth to the nations. Not the immediate effects mind you but the transformation that would begin to occur after the fall of the Roman Empire, 1453 A.D.

Isaiah 61:1 The Spirit of the Lord GOD is on me; because the LORD has anointed me to preach good tidings to the meek; he has sent me to bind up the brokenhearted, to proclaim liberty to the captives, and the opening of the prison to them that are bound; 2 To proclaim the acceptable year of the LORD, and the day of vengeance of our God; to comfort all that mourn; 3 To appoint to them that mourn in Zion, to give to them beauty for ashes, the oil of joy for mourning, the garment of praise for the spirit of heaviness; that they might be called trees of righteousness, the planting of the LORD, that he might be glorified. 4 And they shall build the old wastes, they shall raise up the former desolations, and they shall repair the waste cities, the desolations of many generations. 5 And strangers (Gentiles) shall stand and feed your flocks, and the sons of the alien shall be your plowmen and your vinedressers. (Meaning people of all nations would be pastors and prophets working in the field of the Lord, the world, as ministers of the Gospel.) 6 But you shall be named the Priests of the LORD: men shall call you the Ministers of our God: you shall eat the riches of the Gentiles, and in their glory shall you boast yourselves. 7 For your shame you shall have double; and for confusion they shall rejoice in their portion: therefore in their land they shall possess the double: everlasting joy shall be to them. 8 For I the LORD love judgment, I hate robbery for burnt offering; and I will direct their work in truth, and I will make an everlasting covenant with them. 9 And their descendants shall be known among the Gentiles, and their offspring among the people: all that see them shall acknowledge them, that they are the seed which the LORD has blessed. 10 I will greatly rejoice in the LORD, my soul shall be joyful in my God; for he has clothed me with the garments of salvation, he has covered me with the robe of righteousness, as a bridegroom decks himself with ornaments, and as a bride adorns herself with her jewels. 11 For as the earth brings forth her bud, and as the garden causes the things that are sown in it to spring forth; so the Lord GOD will cause righteousness and praise to spring forth before all the nations. (Meaning, the Word of God will transform the nations. As it has been and will continue to.}

Isaiah 60:1 Arise, shine; for your light is come, and the glory of the LORD is risen on you. 2 For, behold, the darkness shall cover the earth, and gross darkness the people: but the LORD shall arise on you, and his glory shall be seen on you. 3 And the Gentiles shall come to your light, and kings to the brightness of your rising. 4 Lift up your eyes round about, and see: all they gather themselves together, they come to you: your sons shall come from far, and your daughters shall be nursed at your side. 5 Then you shall see, and flow together, and your heart shall fear, and be enlarged; because the abundance of the sea shall be converted to you, the wealth of the Gentiles shall come to you. (The "sea" is an illustration of the nations.)

Please keep in mind this is no where close to a complete list if these scriptures. Especially if you include the volumes of scripture written in code, using illustrations on the subject. Here are some additional articles that delve into the salvation of the nations.
Bible Symbolism in Genesis
The Parables about the Government of God
What is the Government of God
End time Prophecy

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