The Israeli and Palestinian Prime Ministers began talks Thursday, as part of preparations for a summit in Jordan next week with President Bush.
Israeli Prime Minister Ariel Sharon and his Palestinian counterpart Mahmoud Abbas are holding their second round of talks in two weeks.
The two leaders, who are meeting at Mr. Sharon's office in Jerusalem, are discussing the U.S. backed "road map" to peace plan.
It calls for the end of the Israeli-Palestinian conflict and the establishment of a Palestinian state by 2005.
The meeting of the two leaders is also shaping up as a preparation for the summit with President Bush, expected to take place next week in the Jordanian Red Sea resort of Aqaba.
Palestinian officials said they would demand an explicit statement from the Israelis, stating that they recognize the right of Palestinians to live in their own state.
Israeli officials, speaking on condition of anonymity, said Israel was ready to issue such a statement, but only after the Palestinians take efforts to halt violent attacks against citizens of the Jewish state.
The first phase of the "road map" calls for statements from both sides renouncing violence and recognizing each others' rights to security and statehood.
Ahead of their talks, Mr. Abbas also said he expected to soon reach an agreement with Hamas, the Islamic Resistance Movement, to halt attacks against Israelis.
A spokesman for Hamas said the group was considering a temporary cease-fire.
A leader of the Islamic Jihad says that such an agreement might be possible if Israel stops its policy of assassinating Palestinian militants and also releases Palestinian prisoners.