Psalm 2 says that Zion, as part of Jerusalem, is the centre of the rulership as promised by God:
6 “Yet I have set my King on my holy hill of Zion.”
Mount Zion is described as God’s chosen city in Psalm 48:
1 Great is the LORD, and greatly to be praised,
in the city of our God, in his holy mountain.
2 Beautiful in elevation, the joy of the whole earth,
is Mount Zion, on the north sides,
the city of the great King.
The prophets Jeremiah and Micah speak of the world being ruled from Jerusalem at a time of peace:
17 At that time they will call Jerusalem ‘The LORD’s Throne;’ and all the nations will be gathered to it, to the LORD’s name, to Jerusalem. They will no longer walk after the stubbornness of their evil heart.
1 But in the latter days,
it will happen that the mountain of the LORD’s temple will be established on the top of the mountains,
and it will be exalted above the hills;
and peoples will stream to it.
2 Many nations will go and say,
“Come! Let’s go up to the mountain of the LORD,
and to the house of the God of Jacob;
and he will teach us of his ways,
and we will walk in his paths.”
For the law will go out of Zion,
and the LORD’s word from Jerusalem;
3 and he will judge between many peoples,
and will decide concerning strong nations afar off.
They will beat their swords into ploughshares,
and their spears into pruning hooks.
Nation will not lift up sword against nation,
neither will they learn war any more.
The prophet Zechariah tells of the sanctions that will be imposed on nations who don't respect the rule from Jerusalem:
16 It will happen that everyone who is left of all the nations that came against Jerusalem will go up from year to year to worship the King, the LORD of Armies, and to keep the feast of booths. 17 It will be, that whoever of all the families of the earth doesn’t go up to Jerusalem to worship the King, the LORD of Armies, on them there will be no rain. 18 If the family of Egypt doesn’t go up, and doesn’t come, neither will it rain on them. This will be the plague with which the LORD will strike the nations that don’t go up to keep the feast of booths. 19 This will be the punishment of Egypt, and the punishment of all the nations that don’t go up to keep the feast of booths.
Jesus identifies Jerusalem as an important city:
34 but I tell you, don’t swear at all: neither by heaven, for it is the throne of God; 35 nor by the earth, for it is the footstool of his feet; nor by Jerusalem, for it is the city of the great King.