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“Let me be clear: this program is not being implemented on a first-come-first-serve basis,” he said.

The government hopes that banks accepting the government funds will expand their own lending to businesses and individual borrowers. Some private analysts have questioned whether banks who have strong capital bases will accept the government money and the restrictions on executive pay and dividend payouts that come with it.

Mr. Paulson stressed that the plan has been designed so that healthy banks will want to participate.

“This program is designed to attract broad participation by healthy institutions and do so in a way that attracts private capital to them as well,” he said.

Department officials said they would announce transactions under the program within two days, but would not reveal when a bank had been turned down. They said a decision by the government to invest in a bank did not shield the lender from the pressures of the marketplace.

“An investment doesn’t say anything about whether a bank will be allowed to fail,” a senior regulatory official, speaking on background, told reporters.

President Bush on Monday reiterated his commitment to the program.

“If I felt that the crisis could be contained in Wall Street, then I’d have taken a different course of action,” said Mr. Bush during a visit to Alexandria, La. “But the crisis that is gripping this country, and still has a grip on this country.”

Meanwhile on Monday, the new chief executives of Fannie Mae and Freddie Mac are trying do more to stop the home foreclosures hammering the housing market, but said it still might take years for real estate to recover in some cities.

“I don’t think there is any magic bullet in regards to overbuilt markets” like Miami and parts of California, Nevada and Arizona, said Freddie Mac CEO David Moffett at the Mortgage Bankers Association’s annual convention Monday.

The two companies have applied to manage some of the mortgage assets under the $700 billion government rescue program, a person familiar with the matter said Monday. The person declined to be identified because the companies’ bids are not yet public

• David R. Sands contributed to this report, which was based in part on wire service reports.