WASHINGTON — The emerging consensus in Washington, Jerusalem and European capitals is to starve any Palestinian Authority run by Hamas. The emerging dispute is over what “starve ” means.

“The Hamas party has made it clear that they do not support the right of Israel to exist, and I have made it clear so long as that’s their policy, that we will not support a Palestinian government made up of Hamas, ” President Bush said before a Cabinet meeting Monday.

Earlier, in an interview on CBS’s “Face the Nation, ” he was explicit: “Aid packages won’t go forward. “

It sounds unequivocal, but a number of arguments have already erupted over how hard to squeeze the Palestinians for electing a terrorist group to a landslide victory.

One is whether to utterly cut off the Palestinians, or to maintain life support through emergency humanitarian assistance. Another is how soon to end assistance. And finally, there’s the question of whether moneys that Israel owes the Palestinians have the same status as assistance.

In London, Condoleezza Rice, the U.S. secretary of state, extracted a pledge Monday from the other members of the “Quartet ” guiding the Middle East peace process — the United States, the European Union, the United Nations and Russia — to link assistance to a set of conditions.

“The Quartet concluded that it was inevitable that future assistance to any new government would be reviewed by donors against that government’s commitment to the principles of nonviolence, recognition of Israel, and acceptance of previous agreements and obligations, ” the statement said.

That matched the conditions for Israeli cooperation with a Hamas-run Palestinian Authority outlined over the weekend by Ehud Olmert, the acting Israeli prime minister, in a conversation with Kofi Annan, the U.N. secretary-general.

The United States has its work cut out for it trying to keep the international community in line, said Dennis Ross, the top Middle East envoy in the Clinton administration.

“The international community cannot relax its basic posture, ” Ross said Monday at a forum of the Washington Institute for Near East Policy, a think tank. “The administration will have to conduct an ongoing diplomacy that is intensive. “

Russian President Vladimir Putin has already said aid should be unaffected by the election of Hamas.

Rice said humanitarian assistance would continue.

“The Quartet here today has been quite clear that we have deep concern for the Palestinian people and for their well-being; that we’re mindful of their needs, ” she said. “We have noted we’re particularly mindful also of their humanitarian needs and everyone wants to see those needs met. “

But that view could meet resistance on Capitol Hill.

A bill slated to be introduced this week by U.S. Rep. Anthony Weiner (D-N.Y.) would “prohibit United States assistance for the Palestinian Authority and for programs, projects, and activities in the West Bank and Gaza. “

Cutting off “programs, projects, and activities in the West Bank and Gaza ” effectively bans the emergency humanitarian assistance that Rice wants to continue, congressional officials say.

Of $1.5 billion in direct U.S. assistance received by the Palestinians since 1993, $371 million has been in humanitarian aid and emergency response. The rest has gone to reconstruction projects, health and social services and promoting democracy. All of it, however, because of congressional restrictions, bypasses the Palestinian

Authority and goes to direct-assistance programs.

Weiner’s bill also could stop Bush from using a national security waiver for humanitarian aid by making illegal any assistance to the Palestinian areas. Bush has used the waiver three times in recent years to get a total of $90 million to the Palestinians without undergoing stringent congressional oversight procedures.

Weiner, who is close to the Zionist Organization of America, is often a lonely voice for the most severe measures in dealing with the Palestinians. But given the climate since the Hamas landslide, congressional staffers say, his bill stands a chance of passing.

“He didn’t have the backing before the election, but who knows how many people would view this as a viable alternative now, ” said one staffer, who spoke anonymously because the bill has yet be formally introduced.

The American Israel Public Affairs Committee, the pro-Israel powerhouse, had yet to weigh in on whether it would support Weiner’s bill. Americans for Peace Now has already said that its own call to cut off Hamas does not extend to humanitarian assistance to the Palestinians.

Weiner’s bill is competing with two other legislative measures promoted separately by Reps. Ileana Ros-Lehtinen (R-Fla.) and Vito Fossella (R-N.Y.) and a non-binding resolution in the Senate introduced last week by Sen. John Thune (R-S.D.)

All of those initiatives leave open the possibility of continued humanitarian assistance, but shut down all other forms of assistance unless Hamas recognizes Israel, swears off violence and disarms terrorists — the same conditions put forth by Olmert and the Quartet.

The administration has signaled that it wants to keep this fight out of Congress for now, but it faces a battle over timing: Whatever their differences, all of the congressional bill sponsors want to cut off Hamas now.

The Bush administration has, by contrast, joined other members of the Quartet in saying assistance will continue while the interim government is being led by Mahmoud Abbas, the P.A. president and a relative moderate favored by Israel and the United States, and does not include Hamas..

“We are mindful of the needs of the caretaker government and reviewing obligations toward that government, ” State Department spokesman Adam Ereli said. It could be weeks before the new government forms and aid formally ends. The White House said it was encouraged by Abbas’ re-commitment to the peace process.

Olmert expressed understanding for that position, but also voiced concern that in a matter of weeks, terrorists would appropriate money now headed for the Palestinians.

“We are, of course, very sensitive to Abu Mazen’s authority and position, but in the circumstances that have been created, we have to be very cautious, ” Olmert said Monday after meeting with German Chancellor Angela Merkel. Abu Mazen is the name by which Abbas is commonly known.

Olmert said he was considering withholding customs duties, salary taxes and valued-added tax accrued by Israel from Palestinian laborers and businesses.

“I have no intention of allowing the transfer of funds that will be used for terrorism, ” he said.

Israeli Brig. Gen. Mike Herzog, currently a visiting fellow at the Washington Institute for Near East Policy, said Israel had compelling security reasons for keeping the money out of P.A. hands, but suggested that it could be hard to make the case long-term.

“It’s their money,” he said at the Washington Institute forum.