It said the chief negotiators, Israeli Foreign Minister Tzipi Livni and former Palestinian prime minister, Ahmed Qurei, have met in Jerusalem for initial talks intended to tackle the most problematic issues barring the road to peace - state borders, the fate of Jerusalem and the Palestinian refugees.
Israeli officials said Olmert was seeking a deal that would outline a "framework" for a future Palestinian state with implementation delayed until the Palestinians are able to ensure Israel's security.
Abbas wants a final peace treaty enabling him to declare a Palestinian state by the end of 2008.
"All the issues will be discussed. We told Bush that we will not accept a delay in any of the final-status issues," Abbas was quoted as saying on Sunday.
U.S. President George W. Bush ended on Friday the first part of his eight-day tour of the Middle East, designed to advance the peace process and end the protracted conflict in the region.
Bush's first presidential visits to Israel and the Palestinian West Bank were filled with intensive peace negotiations, including talks with Israeli Prime Ehud Olmert and Palestinian President Mahmoud Abbas.
Before leaving Israel for Kuwait, the U.S. president said he was satisfied with the progress of Israeli-Palestinian peace talks resumed at the U.S.-hosted Middle East conference in November and said the sides could conclude a peace deal leading to the establishment of a Palestinian state by the end of 2008.
At the same time, Bush said that an Israeli-Palestinian peace deal would require "painful political concessions" from both sides and a commitment to the so-called Road Map, first outlined in 2002.
Talks between Israelis and Palestinians have been stalled for almost seven years, with no progress made so far on key issues such as borders established before the Arab-Israeli war of 1967, Palestinian claims to East Jerusalem, the plight of Palestinian refugees, and Israeli settlements in the West Bank.
The Palestinians claim all of the West Bank and east Jerusalem, both seized by Israel in the 1967 war. Israel wants to keep parts of east Jerusalem and the West Bank.
During his visit, Bush called for an end to the Israeli "occupation" of Palestinian lands and a resolution for Jerusalem's status and urged President Mahmoud Abbas to curb terrorist and rocket attacks on Israel by Islamists.
He highlighted Hamas, the radical Palestinian group that seized control of the Gaza Strip in June 2007, as a major hindrance to the peace process.
His talks with Israeli officials also focused on the Iranian nuclear program. Bush said that until Tehran stopped uranium enrichment, the Islamic Republic remained a "threat to world peace."
Bush promised to return to Israel in May to attend the celebration of Israel's 60th anniversary and boost the Mideast peace process.
The U.S. president is set to fly from the United Arab Emirates to Saudi Arabia on Monday, before heading on to Egypt in his continuing bid to secure Arab support for his Israel-Palestinian peace effort.
