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.

“We have limited options, and most of them are bad,” said Martin S. Indyk, the former United States ambassador to Israel. 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. In public comments on Wednesday, Tony Snow, the White House spokesman, said that the hope of averting a wider civil war remained largely in the Palestinians’ hands.

“Palestinians are going to have to sort out their politics and figure out which pathway they want to pursue — the pathway toward two states living peaceably side by side or whether this sort of chaos is going to become a problem,” Mr. Snow said.

A senior administration official said that much depends on whether Mr. Abbas decides to continue to fight Hamas, or to surrender to the Islamist group’s demands that he turn over control of the Palestinian security apparatus. “It’s up to Abu Mazen,” the official said, referring to Mr. Abbas.

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.

“He has the power of the presidency, it’s within his power to do that,” the official said, insisting on anonymity because he was not authorized to speak publicly on the issue.

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. “There appears to be a near-total takeover of Gaza by Hamas, which could create a major danger because it would result in an Iranian-backed terrorist state on our doorsteps, between us and Egypt,” Sallai Meridor, Israel’s ambassador to the United States, said in an interview. “We are watching the developments very seriously.”

Mr. Indyk, who is head of the Brookings Institution’s Saban Center for Middle East Policy, argued that such a development could have consequences far beyond the carnage of a civil war between rival Palestinian factions.

“What would happen is that Hamas would take over and Gaza will be a full terrorist state, right on the fault line of the Western world,” Mr. Indyk said. “We should all understand what the stakes are here. It will be a haven for all the bad guys — Hezbollah, Islamic Jihad.”

Equally alarming to Bush administration officials is the prospect that if Hamas does not take over control of Gaza, and the fighting there continues, more of Gaza’s young and increasingly frustrated population might be driven into the embrace of Al Qaeda, a rival of Hamas that, until now, had largely been shunned in Gaza.

“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.”

President Bush had been planning an address later this month to bolster Secretary of State Condoleezza Rice’s recent attempts to broker a peace deal between Mr. Abbas and Prime Minister Ehud Olmert of Israel. But it was unclear on Wednesday whether the recent events in Gaza would upend those plans. Mr. Olmert is supposed to visit Washington next week, and State Department officials said Ms. Rice might soon travel to the region.

Israeli and some Fatah officials have appealed for an international force — possibly under the auspices of the United Nations — to try to restore order in Gaza. But Middle East experts say that few countries are willing to send troops into the increasingly lawless territory, and Bush administration officials expressed little interest on Wednesday in supporting such a force.

Beyond that, administration officials were weighing the possibility of trying to contain the mayhem in Gaza by pressuring Egypt to seal the tunnels leading from its territory into Gaza; American and Israeli officials say the tunnels are often used to smuggle weapons to Hamas.

One administration official suggested Wednesday that the United States might then try to prod Israel into taking down Israeli settlements in the West Bank as a way to shore up Mr. Abbas and demonstrate to the Palestinian population that the diplomatic route favored by Mr. Abbas can bear more fruit than the Hamas way of open resistance to Israel.