President Bush offered Monday to meet at the White House with newly elected Palestinian leader Mahmoud Abbas (search), putting out a welcome mat that was never there for Yasser Arafat (search).

Bush also congratulated Abbas in a telephone call and said, according to a spokesman, that he envisioned "a day when he and president-elect Abbas and Israel's leaders could stand together and say, `We have peace."'

Still, Bush gave no sign that he was relenting in the demands he had made of Abbas' late predecessor -- that the Palestinian leader fight terror against Israel and put together a strong security system to support that stance.

Bush extended an invitation for Abbas to visit the White House when Abbas "felt it was a good time to come," said press secretary Scott McClellan. They did not discuss specific dates.

Proposals by Europeans and others that Bush jump in quickly to press for an Israeli rollback on the West Bank (search) apparently did not impress the administration, despite the emergence of a Palestinian leader who has called for an end to the violent uprising against Israel.

British Prime Minister Tony Blair's offer during a visit to Ramallah (search) to host a one-day Mideast conference did draw support from the administration as a way to promote Palestinian democracy. The president does not plan to attend but is likely to send a top official to London for the parley, a U.S. official said.

Bush is hopeful the conference will help inspire democratic change within the Palestinian movement, said the official, speaking on condition of anonymity.

An Abbas meeting with Bush at the White House would not be their first.

When Abbas was prime minister of the Palestinian Authority (search), before a falling out with Arafat, he visited the White House for a working lunch and news conference in July 2003. He also attended a summit with Bush and Israeli Prime Minister Ariel Sharon in Aqaba, Jordan, that June.

Still in place after Sunday's election is the U.S.-backed "roadmap" for peacemaking, which former American mediator Dennis B. Ross (search) said could be a vehicle for progress if more of its principles were implemented.

These include Palestinian arrests of violent militants and the elimination of illegal Israeli outposts on the West Bank, Ross said at the Washington Institute for Near East Policy.

Bush, at the White House, said, "I think it's going to be very important for Israel to fulfill its obligation on the withdrawal from the territories that they have pledged to withdraw from."

"It is essential that Israel keep a vision of two states living side-by-side in peace, and that, as the Palestinians begin to develop the institutions of a state, that the Israel government support the development of those institutions," Bush said.

Unlike some analysts, Ross recommended a gradual approach, including assignment of a senior State Department official to work exclusively on the Israeli-Palestinian conflict and talk regularly to both sides.

Former national security adviser Zbigniew Brzezinski, on the other hand, proposed last week that Bush make specific recommendations for a resolution. He said these should include an end to all Jewish settlements except a cluster near Jerusalem and demilitarization of the Palestinian state that emerges.

Bush, speaking to reporters in the Oval Office, gave no hint of taking on any of these ideas. He confined his remarks to saying he was heartened by the Palestinian elections and offering his congratulations to Abbas.

"I look forward to welcoming him here to Washington if he chooses to come here," the president said. He referred to Abbas as Abu Mazen (search), as he is commonly known among Palestinians.

The fact that the president has met nine times with Sharon and has endorsed the prime minister's demands for an end to terror as a precondition to peacemaking has hammered home Bush's scorn for Arafat as a failed and corrupt leader unable to deliver Palestinian statehood and peaceful coexistence with Israel.

Last month, as Arafat's succession was taking shape, Bush ruled out "shortcuts" to a peace accord. He said he and his administration would be on the lookout for evidence of democracy taking root and for a concerted effort to dismantle terror groups.

Israeli leaders have welcomed Abbas' victory but have also said they will watch closely how hard he tries to subdue militants.