The biggest question is how Abbas, a U.S.-backed moderate, could make good on any peace promises to Israel when he effectively governs only in the West Bank while Hamas Islamists control the Gaza Strip.
Politically weak, Abbas is hoping Bush's visit to Ramallah will boost his own standing among Palestinians, who are desperate for progress towards an end to Israeli occupation and fulfilment of their dream of an independent state.
Bush's first presidential trip to Israel and the Palestinian territories is aimed at nudging the two sides into serious negotiations after they pledged at a U.S.-sponsored conference in November to try to forge a two-state deal before he leaves office a year from now.
But Bush's chances of success are considered slim, given doubts about his commitment and whether he can act as an even-handed peace broker between close U.S. ally Israel and the Palestinians.
He held talks with Israeli Prime Minister Ehud Olmert in Jerusalem on Wednesday, saying he was "very hopeful" about prospects for peace. But he also acknowledged: "I'm under no illusions. This is going to be hard work."
Urging both sides to make concessions, Bush said Olmert, also politically weak, must meet Israel's obligation to dismantle small settler "outposts" set up without government authorisation.
But while acknowledging the need to shore up Abbas's fragile position, Bush reserved some of his toughest language for the Palestinian leader, saying he would press him to do more to rein in anti-Israel militants.
