The opposition has criticised Mr Barak for straying from a widely-held belief in Israel that it has exclusive sovereignty over an undivided Jerusalem.
Referring to the Arabic name for the city, Mr Barak said: "It will be Jerusalem and al-Quds, one next to the other, as two capitals."
He was speaking in an interview in Jerusalem Post published on the same morning as serious clashes broke out on the Mount, as Palestinians protested against a tour of the compound by Israeli opposition leader Ariel Sharon.
The opposition has criticised Mr Barak for straying from a widely-held belief in Israel that it has exclusive sovereignty over an undivided Jerusalem.
Israel captured the east side of Jerusalem in 1967 and, under international law, has been illegally occupying the territory ever since.
Uncertain future
While he outlined his vision of a future peace deal, Mr Barak also expressed uncertainty about whether it was feasible.
"I am not sure that there will be an agreement, because I am not sure there is a partner ready for historic decisions," he said.
"But if there is an agreement it will include an end to the conflict, permanent borders for Israel recognised by the world, 80% of the settlers under Israeli sovereignty in permanent blocks, security arrangements, principally along the eastern border, and Jerusalem bigger than ever since King David," he added.
Mr Barak also stressed that no Jewish prime minister would agree to transfer the sovereignty of the Temple Mount to the Palestinians or to an Islamic body.
Shades of 1995
The Jerusalem Post said it asked Mr Barak if he would agree to transfer site to an international body like the United Nations, or to specific Muslim countries, but he replied "he did not want to discuss the issue at this point".
He also said that a partial peace agreement leaving the question of Jerusalem for future discussion would be possible.
The paper said the Israeli leader's position bore a striking resemblance to an agreement reached between Israeli and Palestinian negotiators Yossi Beilin and Abu Mazen in 1995.