Bush said that support for Hamas, which seized Gaza from the forces that back Abbas on June 15, would be a victory for the group's "foreign sponsors" in Syria and Iran and "would crush the possibility of a Palestinian state".
The US president said Israel, the Palestinians and their Arab neighbours could do more to help revive Middle East peace prospects and called for an international conference.
"The refusal by the US, EU et al to deal with Hamas reflects their disrespect for the wishes of the Palestinian people"
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"The world can do more to build the conditions for peace," he said, adding that Condoleezza Rice, the US secretary of state, will chair the gathering and that attendance will be limited to states that back the creation of a Palestinian state, reject violence, and recognise Israel.
The plan won instant backing from Israel and Abbas, but swift condemnation from Hamas, whose spokesman, Ismail Radwan, told AFP: "We condemn this American conference which aims to serve the interests of the Zionist enemy."
"The conference will lead to increased pressure on Mahmoud Abbas and separate the Gaza Strip more deeply from the West Bank while sowing division among Palestinians," he said.
Bush also urged Arab nations to end "the fiction that Israel does not exist," curb anti-Israel rhetoric in their media and send cabinet-level officials to the Jewish state.
And Bush pushed Olmert to continue to release Palestinian tax revenue to Salam Fayyad, the Palestinian prime minister, halt Israeli settlement expansion and dismantle unauthorised outposts.
Israelis "should be confident that the United States will never abandon its commitment to the security of Israel as a Jewish state and homeland for Jewish people," he said.
Bush also hailed the talks between Olmert and Abbas, as a senior Israeli official said that the prime minister had pledged to free 250 Palestinian prisoners in a goodwill gesture to the Palestinian leader.
But while welcoming the release, the Palestinians said the freeing of 250 prisoners out of the more than 11,000 currently held in Israeli jails was not enough.
Bush also announced a direct US contribution of $80m to help Abbas reform his security services. Two US officials said the money was being shifted from Gaza to Fayyad's government.
More US aid will come when former British prime minister Tony Blair, now the envoy for the Middle East "quartet" of the United States, United Nations, European Union, and Russia, reports success in building a plan for bolstering Palestinian security and political institutions.
"With the proper foundation, we can soon begin serious negotiations toward the creation of a Palestinian state," said Bush.
But "we're not going to announce a dollar amount for a plan that has yet to be elaborated or announced," a senior US official said on condition of anonymity.
The Quartet is to meet in Lisbon, the Portuguese capital, on Thursday to take stock after Abbas appointed a new government following the takeover of Gaza by Hamas.
Bush backs Abbas
It is to be the first meeting between the quartet's chief diplomats, including Rice, and Blair, who was named to the envoy post shortly after stepping down as British leader on June 27.
|Bush telephoned Abbas to reaffirm|
the US support to the president [AP]
But the US, which sees Blair's job as preparing the ground for the establishment of viable Palestinian institutions, is reluctant to define for him any political mission.
Meanwhile President Bush telephoned Abbas on Monday to reaffirm Washington's support for the Palestinian president, a spokesman for Abbas said.
The two men spoke after Bush called for an international conference to revive Middle East peace talks.
"President Bush expressed his support for president Abbas and for efforts to relaunch the peace process through this conference" in the autumn,
Nabil Abu Rudeina told reporters.
"President Bush also expressed his support for the Palestinian government led by Salam Fayyad," he added in reference to the prime minister.