JERUSALEM (CNN) -- Israeli Prime Minister Ehud Olmert and Palestinian President Mahmoud Abbas agreed Sunday to authorize peace talks, which could begin Monday, according to the offices of both leaders.
Olmert and Abbas said they would tell negotiating teams to "conduct direct and ongoing negotiations on all final status" and core issues, the prime minister's office said.
Israeli Foreign Minister Tzipi Livni is slated to meet with former Palestinian Prime Minister Ahmed Qorei on Monday, said Aryeh Mekel, a spokesman for Livni.
However, he said the meeting may only be to discuss procedural issues regarding the negotiations, rather than the core issues themselves.
The "core issues" include Israeli settlements in the West Bank; the right of Palestinian refugees to return to Israel; the future status of Jerusalem; borders; security and water supply.
The announcement regarding the negotiations came three days after President Bush's visit to Israel and the Palestinian territories. Much of Bush's eight-day trip to the Mideast is centered on the ambitious task of sealing an elusive peace agreement between the two sides. Watch more about Bush's plans in the Middle East »
During his stay in Israel, Bush called on Israeli and Palestinian leaders to make "painful" concessions in reaching a peace agreement -- including dismantling "terrorist infrastructure" and ending Israel's "occupation" of Palestinian territory.
"There should be an end to the occupation that began in 1967," Bush told reporters in Jerusalem on Thursday. "The agreement must establish a Palestine as a homeland for the Palestinian people, just as Israel is a homeland for the Jewish people."
The president called on Palestinians to confront terrorists. "Security is fundamental," he said. "No agreement and no Palestinian state will be born of terror."
Abbas called Thursday on Israel to comply with the terms of the road map, a U.S.-supported peace plan agreed upon in 2003. Under the road map, Israel must halt West Bank settlement activity and Palestinians must dismantle militant groups. Israeli leaders have said they are committed to the road map, and have called on Palestinian leaders to abide by their obligations.
"We are fully satisfied with the outcome that we reached through this visit with President Bush," Abbas said.