WASHINGTON, June 13 — For two years, the United States has tried to choke off Hamas, the militant Islamic group that has been ascendant in Gaza and the West Bank, while throwing limited aid and support to Fatah, its more moderate Palestinian rival. Now, with Fatah, the party of the Palestinian president, Mahmoud Abbas, on the verge of collapse in Gaza, Washington is facing a shrinking menu of alternatives...

America’s options are limited in part because its role has been limited, with the Bush administration pursuing what for the most part has been a hands-off policy toward the Palestinians...

Administration officials were pushing Mr. Abbas to dissolve the power-sharing agreement between Fatah and Hamas that set up the Palestinians’ national unity government, dismiss the entire government and use the power of the Constitution to call for new elections...

But several Palestinian Authority officials in Ramallah indicated Wednesday that Mr. Abbas was considering giving Hamas control over the Palestinian Authority’s security forces in Gaza, a move that would ostensibly cede the territory to Hamas and leave Mr. Abbas with authority solely over the West Bank.

“There are a lot of people now who are angry and are saying, ‘Let Hamas govern Gaza, let Gaza go to hell,’ ” said Ghaith al-Omari, a former foreign policy adviser to Mr. Abbas who is now a fellow at the New America Foundation, a public-policy institute in Washington.

But that is a prospect that Israel and the United States fear could lead to a situation in which Gaza becomes a breeding ground for terrorists...

“The central discipline of both Fatah and Hamas has broken down, and the public is taking the attitude of ‘a plague on both of their houses,’ ” said Daniel Levy, a former peace negotiator in Israel who is now a senior fellow at the New America Foundation. “We will soon be looking back with misty-eyed poignancy on the idea of driving the Palestinians into the hands of Hamas. What we will have done, actually, is driven them into the hands of Al Qaeda...”

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