But many doubt differences can be overcome now, as Bush seeks to burnish his legacy in the Middle East after five years of war in Iraq. Olmert is politically weak and Abbas cannot control the Gaza Strip, which Hamas Islamists seized in June.
COMPROMISE
Bush reiterated in the keynote statement a vision of territorial compromise he first charted in a policy letter to then-Israeli Prime Minister Ariel Sharon in 2004, advocating mutually agreed changes in armistice lines set in 1949 after fighting with Arab armies that accompanied Israel's foundation.
Bush said he had urged Abbas and Olmert, whom he met on Wednesday and again on Thursday evening, "to make sure their teams negotiate seriously, starting right now".
His use of the term "peace treaty" was seen by some as an indication he was not ready to settle for a vaguer "framework agreement" which Israeli and Palestinian officials have said Olmert thinks is all that is feasible before Bush steps down.
Bush also reaffirmed a U.S. commitment to a 2003 peace "road map" under which Israel was to halt settlement activity and Palestinians were to crack down on militants.
"On the Israeli side, that includes ending settlement expansion and removing unauthorised outposts. On the Palestinian side that includes confronting terrorists and dismantling terrorist infrastructure," the president said.
"Security is fundamental. No agreement and no Palestinian state will be born of terror. I reaffirm America's steadfast commitment to Israel's security."
The White House announced Bush had appointed U.S. Lieutenant-General William Fraser to monitor steps both sides are supposed to take under the road map as part of a peace process revived at the international summit in Annapolis.
Preparing to head to the Gulf on Friday, Bush said he would urge Arab states to "reach out" to Israel.
Speaking earlier at the Muqata compound where the late Palestinian leader Yasser Arafat was besieged by Israeli forces just a few years ago, Abbas hailed Bush as the first U.S. president to commit fully to back a Palestinian state.
After the meeting, Bush flew by helicopter to the West Bank city of Bethlehem to visit the Church of the Nativity, built over the traditional birthplace of Jesus.
There the president, a devout Christian, spoke of his hope for a divine gift of freedom for all people and an end to the Israeli walls and checkpoints that ring the Palestinian town.
