Olmert, 62, resigned on September 21 amid corruption allegations, and was replaced by Foreign Minister Tzipi Livni, 50, as the ruling party's leader last week.
In an interview with the Yediot Aharonot newspaper, published on the eve of the Jewish New Year, Olmert said: "We should quit almost all territories, including East Jerusalem and the Golan Heights."
East Jerusalem, which was part of Jordan from 1948, and the formerly Syrian Golan Heights, were annexed by Israel in the 1967 six-day war. Their status, along with Jewish settlements in the West Bank, have proved the main obstacles to reaching an Israeli-Palestinian peace deal.
"In exchange for the territories we will retain, we will have to cede lands within the state of Israel," said Olmert, who resumed talks with Palestinians and revived dialogue with Syria last year.
