Olmert and Mahmoud Abbas, the Palestinian president, agreed at a meeting in the United States last November to push for a comprehensive peace deal before the end of the year.
Yediot Ahronot noted that the remarks in its "legacy interview" go further than any the prime minister made before he effectively became a lame duck in September.
"I am not trying to justify retroactively what I did for 35 years. For a large portion of these years, I was unwilling to look at reality in all its depth," Olmert said.
"A decision has to be made. This decision is difficult, terrible, a decision that contradicts our natural instincts, our innermost desires, our collective memories, the prayers of the Jewish people for 2,000 years."
Peace talks between the two sides have stalled over the borders of a future Palestinian state, the future status of Jerusalem and the right to return of Palestinian refugees.
The construction of new Jewish settlements in the West Bank and Arab East Jerusalem, which Palestinians see as the capital of a future state, have also proved to be a major obstacle.
"I'd like see if there is one serious person in the State of Israel who believes it is possible to make peace with the Syrians without eventually giving up the Golan Heights"
Israeli prime minister
According to Western and Palestinian officials, Olmert has previously proposed an Israeli withdrawal from some 93 per cent of the occupied West Bank. Israel pulled out of the Gaza Strip in 2005.
In exchange for settlement enclaves, Olmert has suggested handing over a desert territory adjacent to the Gaza Strip, as well as land on which to build a transit corridor between Gaza and the West Bank.
"We will leave a percentage of these territories in our hands, but will have to give the Palestinians a similar percentage, because without that there will be no peace," Olmert said in Tuesday's interview.
Olmert has previously argued that the issue of Jerusalem be considered at a later date because the difficulties in reaching an agreement.
But on Tuesday he said that giving up parts of the city was critical to securing Israel's security.
"Whoever wants to hold on to all of the city's territory will have to bring 270,000 Arabs inside the fences of sovereign Israel. It won't work," he said.
Saeb Erakat, a senior adviser to Abbas, said Israel must "translate these statements into reality" if it is serious about wanting to achieve a peace deal.
"We haven't seen these statements translated into a piece of paper, into a concrete offer," he told the AFP news agency, stressing that "the road to peace is through ending the occupation and [Israeli] settlements in the West Bank".
During his time in office, Olmert reopened indirect negotiations, through Turkey, with Syria after an eight-year freeze.
"I'd like see if there is one serious person in the State of Israel who believes it is possible to make peace with the Syrians without eventually giving up the Golan Heights," he said in the interview.
Israel annexed the territory in 1981, a move never recognised by the world community.
More than 18,000 Syrians, mostly Druze, are left from the Golan's original population of 150,000 people. The region now is home to nearly 20,000 Jewish settlers.