Bush met the two leaders separately, then together, before appearing before the media.
Olmert and Abbas pledged on Tuesday to work towards a lasting peace settlement at the Middle East conference in Annapolis, Maryland.
In depth

Speaking afterwards, Condoleeza Rice, the US secretary of state, said Abbas and Olmert would continue talks after Wednesday's meetings with Bush. 


She said the two leaders would meet again on December 12 and continue discussions every two weeks after that.


Later on Wednesday, she announced the appointment of James Jones, a marine general and former Nato commander, to the post of US liaison between Israel and the Palestinians.


Three-way talks


In his speech at the Annapolis conference, which was attended by delegates from 50 countries including Syria and Saudi Arabia, Bush said that mutual understanding between Israel and Palestinians was key to a peace deal.

"Palestinians and Israelis each understand that helping the other to realise their aspirations is the key to realising their own, and both require an independent, democratic, viable Palestinian state," he said.


Annapolis reaction


He said the Palestinians must improve security and stability in their territories and said the expansion of Israeli settlements, which are illegal under international law, should stop.


He did not mention the most intractable issues of borders, the final status of Jerusalem and the right of return for Palestinian refugees. 


Neither the Palestinians nor the Israelis have indicated they will move from their positions on those points.

Contrasting positions
The attendance at Annapolis of Abbas, who is leader of the Palestinian Fatah party, was in marked contrast to rival party Hamas, which held protests against the conference in Gaza, where it has control.
Hamas does not recognise the Israeli state.

Bush said pointedly at Tuesday's conference that "the United States will keep its commitment to the security of Israel as a Jewish state and homeland for the Jewish people.

Protests against Annapolis erupted again on
Wednesday in the city of Hebron [AFP]
"This settlement will establish Palestine as the Palestinian homeland, just as Israel is the homeland for the Jewish people".

However, Olmert has ruled out the return of Palestinian refugees to their homeland inside Israel.
In a television interview, he said: "No one would think seriously about establishing two states, one Palestinian and another state in which Palestinians become the majority after the return of the refugees to Israel.
"Therefore, the idea is to establish two separate nation states living side by side.
"The state of Israel would of course be Jewish. A Palestinian state would be the natural location for all the Palestinian refugees where they would be settled," he said.
Core issues
Speaking at Annapolis, Abbas listed what would be covered by Wednesday's talks.
"We have to start comprehensive and deep negotiations on all issues of final status, including Jerusalem, refugees, borders, settlements, water and security and others," he said.
He expressed the Palestinians' desire for East Jerusalem to be the capital of "our state".
Olmert said he was aware the geography of the contested region would alter as a result of any peace deal.
"I have no doubt that the reality created in our region in 1967 will change significantly," he said.
"We want peace. We demand an end to terror, incitement and hatred. We are willing to make a painful compromise, rife with risks, in order to realise these aspirations," he said.
Fresh violence

Meanwhile, in the occupied territories, an Israeli air raid killed two Hamas fighters in the south of the Gaza Strip, medics said.


Five others were wounded in Wednesday's raid that targeted Hamas's Executive Force, a paramilitary unit that has acted as police since Hamas seized control of Gaza in mid-June.


An Israeli army spokesman confirmed an aerial attack had been carried out, and said fighters had launched 11 rockets and mortars from the territory into Israel on Wednesday.

In the West Bank, 28 Palestinians were injured in clashes with the Palestinian police.

The clashes broke out in Hebron during the funeral of the young man who was killed on Tuesday by police in a protest against the Annapolis conference.


The police opened fire in the air and wounded two people.


Elsewhere, Israeli gunboats shelled Hamas police positions along the coast of Khan Younis, south of the Gaza Strip, killing two Palestinians and injuring another three, Palestinian medical sources said.


A spokesman for the Israeli army said that the shelling targeted a site of Hamas after firing mortar shells.

Source: Al Jazeera and agencies