Mahmoud Abbas and Ehud Olmert decided this during informal talks hosted by King Abdullah of Jordan in the ancient town of Petra on Thursday.
The meeting was the first between the Israeli and Palestinian leaders in a year.
"I am ready to put on (the) line everything for one purpose, to achieve peace, to make compromise, to pull out of certain territories," Olmert said.
"I pray the Palestinians will have the courage to get rid of extremists and fundamentalists."
Israel has said it will not negotiate with Hamas but may hold talks with Abbas directly.
Olmert and Abbas shook hands and embraced, with the Israeli premier using the ice breaker to apologise for 13 Palestinian civilian deaths in recent Israeli air strikes.
"It is against our policy and I am very, very sorry," he said after a breakfast meeting with Abbas, but he said later Israel would continue striking at Palestinian fighters.
While he had only warm words for Abbas and indicated he would meet with him again, Olmert cautioned against high hopes: Peace talks are unlikely, he suggested, unless the Palestinians' anti-Israel government changes its policy.
King Abdullah II is hosting the
conference in Petra
"I think that Abu Mazen is a genuine person and he comes here with good intentions," Olmert said, using the Palestinian leader's nickname.
"But to the best of my knowledge, he is not the prime minister of the Palestinian Authority."
Speaking in Jerusalem on Thursday evening after returning from Jordan, Olmert repeated his apology from the civilian deaths but said: "Israel will continue to carry out targeted attacks against terrorists and those who try to harm Israeli citizens."
Olmert also singled out Abbas as a partner for talks but said Israel would not negotiate with Hamas, which he said "leans on terror".
The breakfast meeting between Olmert and Abbas took place on the sidelines of a two-day gathering of Nobel Prize winners.
Olmert, Abbas and Abdullah sat at a round breakfast table with the Dalai Lama, a deputy Thai prime minister and Elie Weisel, a Holocaust survivor and the 1986 Nobel Peace Prize winner.
Asked about his handshake with Olmert, Abbas said: "It was very warm, very warm."
After returning to the West Bank city of Ramallah, Abbas said the two "discussed one point - how to prepare for a forthcoming meeting".
He said he will travel to Gaza on Friday to supervise talks between rival factions in attempt to solve a domestic political crisis.
Abbas said he hope the talks would achieve "positive results" and that they would "allow us to present the world with new ideas in order to end the siege imposed on us.