|PIC1|U.S. President George W. Bush faces a balancing act in West Bank talks with Palestinian President Mahmoud Abbas on Thursday, the second day of a Middle East peace mission laden with scepticism.

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.

ROCKET FIRE

Bush spoke after the latest cross-border rocket fire from Gaza wounded one Israeli on Wednesday. Israel responded with a missile strike that killed one militant and two civilians in the northern Gaza Strip.

"As to the rockets, my first question is going to be to President Abbas, what do you intend to do about them?" Bush said at a joint news conference with Olmert.

U.S. officials, however, were at a loss to explain how Abbas could extend his authority to Gaza. The coastal strip has been controlled since June by Abbas's Hamas rivals, who deny Israel's right to exist.

Stephen Hadley, Bush's national security adviser, called the situation in Gaza "pretty depressing".

In the six weeks since Bush relaunched peace talks at Annapolis, Maryland, Palestinians have accused Israel of bad faith for not halting settlement activity.

Palestinian officials said Abbas would renew complaints to Bush about Jewish settlement growth and also demand an easing of Israeli military roadblocks in the West Bank.

Bush's visit to the "muquata" compound is certain to stir memories of the late Yasser Arafat, who spent the last three years of his life virtually confined there by Israeli forces and shunned by the U.S. president as an obstacle to peace. Arafat's tomb lies on the grounds of the Ramallah complex but Bush has no plans to visit it.

Bush will also visit the Church of the Nativity, the traditional birthplace of Jesus, in Bethlehem on Thursday.

Despite scepticism at home and abroad over his peace bid, Bush seems intent on using the waning months of his presidency to try to shape a foreign policy legacy not completely defined by the unpopular war in Iraq.