~ Nearly 3 million Palestinians now essentially have two governments.

WASHINGTON -- President Bush and Israeli Prime Minister Ehud Olmert sided emphatically Tuesday with a weakened Mahmoud Abbas, hoping extra money and warm words would give the moderate leader primacy over the Islamic militant Hamas in the newly divided Palestinian territories.

"He has spoken out for moderation," Bush said at an Oval Office strategy session with Olmert. "He is a voice that is a reasonable voice amongst the extremists in your neighborhood."

"Like you, I want to strengthen the moderates," echoed Olmert, who promised "to make every possible effort to cooperate" with Abbas.

It was not the first time Bush has felt the need to prop up Abbas, but this is a period of particular upheaval and uncertainty.

Bloody street battles in the Gaza Strip ended with Hamas seizing control last week of the tiny coastal territory from Abbas' Fatah security forces. The rout prompted Abbas to evict Hamas from the Hamas-Fatah coalition government, a move Hamas decries as illegal.

Nearly 3 million Palestinians now essentially have two governments. Nearly half are under Hamas control in Gaza, with the rest under Abbas' authority in the inland West Bank. Hamas is sworn to Israel's destruction, while Abbas' Fatah movement seeks peace with the Jewish state.

The response from the United States and much of the rest of the West has been swift: try to shore up Abbas in hopes that the West Bank can be made into a democratic example that would bring along Gaza.

On Monday, the Bush administration resumed aid and full government contacts with the Palestinian government, suspended in 2006 when Hamas won legislative elections. Israel is also likely to free millions in tax revenue it collects on behalf of the Palestinians.

"Our hope is that President Abbas and the prime minister -- [Salam] Fayyad, who's a good fella -- will be strengthened to the point where they can lead the Palestinians in a different direction, with a different hope," Bush said.

Sitting side-by-side in an Oval Office meeting planned well before the Gaza crisis unfolded, Bush and Olmert painted Abbas as the one true leader of the Palestinian people.

Both men called him the "president of all Palestinians" -- an effort to confer at least as much legitimacy on Abbas' 2004 election as president of the Palestinian Authority as on the Hamas legislative wins last year. Olmert said Abbas is "perhaps the only person who was widely elected in a democratic manner by all of the Palestinian people."

Their effort got a lift from a representative of neighboring Arab states. Saudi foreign minister Prince Saud al-Faisal said those countries back Abbas' moves to dissolve the coalition cabinet, declare a state of emergency and outlaw Hamas' armed wing. "The Arab League stands firmly with the president and with the legality," he told CNN.

While the leaders heaped support on Abbas, they sought to further isolate democratically elected Hamas by doing just the opposite.

Olmert said that "many people in the world were astounded by the brutality and the cruelty and the viciousness" of the Hamas fighters. Bush lumped the radical group with the likes of al-Qaida and insurgents in Iraq, calling them "a group of radicals and extremists who are willing to use violence, unspeakable violence sometimes, to achieve a political objective."

Critics have said that the United States helped bring about Hamas' rise by not giving more cash and support to Abbas before the elections. Hamas' surprise victory was credited largely to the services it already had been delivering in its Gaza stronghold.

Bush laid the blame for the current split in the Palestinian territories squarely on Hamas. "They made a choice of violence," he said.

Presidential press secretary Tony Snow said Hamas' recent actions will convince both Palestinians and the world of its true nature, that of a terrorist organization, as listed by Israel, the European Union and the United States. "I can't imagine that killing people in the streets is going to be a big vote-getter," he said.

Still, Olmert was willing to go only so far for Abbas.

Abbas has said that all sides should capitalize on the situation and restart long-stalled peace negotiations. But though the Israeli leader said "there's no question that I want to talk" to Abbas, he also laid out several prerequisites for progress that included implied criticism of his Palestinian counterpart. Olmert's conditions included "a much more credible and serious administration" by the Palestinians, one that will "fight terror in the most effective way."

The chaos in the Mideast also complicates White House plans for outlining Bush's vision for the peace process, an area where the president has been criticized for a lack of focused effort. The White House had hoped to the mark the fifth anniversary of Bush's June 24, 2003, call for a separate, independent Palestine alongside Israel with a major address. That is up in the air now.