While Mr. Paulson has agreed with that argument, the Bush administration is also leaning on foreign governments to pitch in with bailout programs of their own as needed. “We have a global financial system and we are talking very aggressively with other countries around the world, and encouraging them to do similar things, and I believe a number of them will,” Mr. Paulson said on Sunday.

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The request is expected to be discussed during a conference call among Group of 7 finance ministries scheduled for Sunday evening, a European official said.

Allowing foreign banks to participate in the federal rescue package has not yet drawn widespread scrutiny in Congress, where a number of lawmakers, including Senator Christopher J. Dodd, Democrat of Connecticut, have acknowledged that millions of American citizens do business with UBS, the Royal Bank of Scotland, and many other foreign-based banks in the United States.

But a number of lawmakers are wary that such an extension may worsen what could ultimately turn out to be a trillion-dollar bailout for Wall Street.

“I’m skeptical of the bailout, the whole bill is only a couple of pages long,” said Representative Scott Garrett, Republican of New Jersey, who is a member of the House Financial Services Committee. As for the participation of foreign banks, Mr. Garrett said: “I have a concern with it, they probably should be treated differently, but Congress is really not getting any say.”

Christopher Whalen, a managing partner at Institutional Risk Analytics, said that Mr. Paulson needed to justify why a wider bailout was in the national interest.

“Can you imagine the Congress floating a bailout for Deutsche Bank or UBS? It is the responsibility of the German or Swiss government,” he said. “We shouldn’t be bailing them out.”

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While politicians in the United States may emphasize the benefits for banks based overseas, the definition of what is a European or American bank has blurred in recent years with the growth of global giants like HSBC, Barclays and Deutsche Bank.

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Deutsche Bank, for example, became a major player in the United States with its acquisition of Bankers Trust in 2001. It has written down more than $11 billion in investments linked to the subprime crisis.

Barclays, meanwhile, is on course to buy a significant portion of the North American operations of Lehman Brothers, the 158-year-old firm that filed for bankruptcy protection last week, helping to set off the global financial panic that forced Washington to act.

Gaining access to the relief was a top priority for European foreign financial institutions with banking operations in the United States, according to officials in industry and government.

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They argued that the reputation of Wall Street and the United States government would suffer immensely if properly licensed foreign banks in the United States were shut out of the system.

“Who would open a bank again in the United States?” asked one executive of a major European bank who has been following the discussions.

At the same time, it was unclear how much European governments would bow to the Treasury Department’s encouragement to set up national programs to deal with their own vast mortgage problems. Real estate markets in Britain, Spain and Ireland have been particularly hard-hit as their own housing market bubbles — which grew in tandem with America’s — have collapsed.

Other governments have struggled to get budget deficits under control in the last few years. The German government, for example, has discouraged talk of a stimulus package, and British officials said Sunday that they were not working on a plan like that of the United States.

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Robert Kelly, chief executive of the Bank of New York Mellon, said the central bankers around the world would probably be scrutinizing the American bailout proposal. “I would expect every finance minister is looking closely at what is happening in the United States, trying to hypothesize what the impact will be, and is thinking about the tools the Fed and Treasury have used,” he said. “I would not be surprised, and probably expect, some of those tools to be used in Europe as well.”

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If the plan is approved in Congress and is signed into law, the benefits would be large for European banks with licensed operations in the United States, which incurred major losses from mortgage-linked securities.

UBS, the Swiss giant, has been among the hardest-hit institutions in the world; both its chairman and chief executive left amid more than $40 billion in write-downs. Even so, it still retains roughly $20 billion more in potential exposure to the troubled American housing market.

If a battle does develop in Congress over foreign participation, UBS, among others, is poised to make just these arguments. Officials at the Zurich-based giant point out the bank employs more than 30,000 Americans, is listed on the New York Stock Exchange, and owns two broker-dealers registered under United States laws, UBS Securities and UBS Financial Services, better known to Americans as the former Paine Webber unit.

“These are Americans who work in New York,” said one executive who requested anonymity because the American plan was still in development. “And they are working for a bank that was incorporated in the United States.” One senior Wall Street executive said he believed that the proposal would apply to other institutions with regulated American entities. Credit Suisse, for example, includes the old First Boston Corporation, though that name was dropped years ago. He said the biggest issue being debated was what securities would be included in the proposal, and how the actual mechanism to buy them would work.

In Asia, the plan to purchase distressed assets drew little reaction over the weekend. Asian banks generally have not invested significant assets in American mortgage-backed securities.

The bigger question in Asia, bankers said, lies in how the American legislation will affect HSBC, the large British-based bank with significant operations in Asia. The bank’s American subsidiary was a large buyer of mortgages over the last decade, and kept many of these mortgages on its books instead of trying to repackage and resell them as mortgage-backed securities.

Richard Lindsay, a spokesman for HSBC, said that senior management was still evaluating the situation and said it was a “positive step forward but it won’t solve the problems of an overleveraged industry.”