WASHINGTON — Senate negotiators on Monday said they had reached a deal on legislation aimed at helping hundreds of thousands of homeowners in danger of foreclosure by expanding the availability of government-insured mortgages.

The Bush administration, which previously said it would oppose legislation to rescue troubled homeowners, suggested that it was willing to consider the Senate deal because lawmakers had found a way to eliminate any direct cost to taxpayers.

The Senate bill would create an affordable housing fund, financed by the government-sponsored mortgage-finance companies, Fannie Mae and Freddie Mac, and that fund would be used in its first year to provide about $500 million for the foreclosure rescue effort.

Senator Christopher J. Dodd, Democrat of Connecticut and chairman of the Banking, Housing and Urban Affairs Committee, who announced the agreement, said his goal was to create a solid foundation underneath the nation’s depressed housing market.

“The primary goal here is to keep people in their homes, but also to establish a floor, a bottom to all this,” Mr. Dodd said. The foreclosure aid is tied to legislation creating a new regulatory agency to tighten oversight of the government-sponsored mortgage financiers.

The House this month approved a similar foreclosure rescue bill by a vote of 266 to 154, which was cast mostly along party lines. Only 39 Republicans joined Democrats in supporting the bill, many of them from states hit hard by foreclosures.

Under both the House and Senate plans, lenders could limit their losses from potential foreclosures by agreeing to reduce the principal balances of loans at risk of default. The borrowers, many with expensive adjustable-rate loans, could then apply to refinance with a more stable, 30-year, fixed-rate mortgage insured by the government through the Federal Housing Administration.

In addition to paying interest and principal, the lender would pay a monthly insurance fee, which would go into a fund to protect taxpayers from losses.

The Congressional Budget Office has estimated that under the House bill, up to 500,000 mortgages would be refinanced over the next five years, at a cost to taxpayers of about $2.7 billion.

Mr. Dodd said that his bill included several changes, including shortening the life of the foreclosure assistance plan to three years, which would reduce the cost to about $500 million. He said that roughly the same number of mortgages could be refinanced.

That $500 million would be taken from a new affordable housing fund, which would collect slightly less than half a cent on every dollar of mortgages purchased by Fannie Mae or Freddie Mac.

That fund, proposed by Senator Jack Reed, Democrat of Rhode Island, would continue to exist after the foreclosure assistance plan ended, with the money directed to creating affordable housing, including low-income rental housing.

Rhode Island has one of the highest foreclosure rates on subprime mortgages in the country.

A day before the House approved its foreclosure rescue plan, President Bush had flatly threatened to veto the bill, saying it would put taxpayer money at risk and “reward speculators and lenders.”

Many lawmakers interpreted the president’s remarks as a signal to Senate Republicans to kill the housing legislation before it could reach Mr. Bush’s desk.

But the White House reacted with a more agreeable tone to news of the deal between Mr. Dodd and Senator Richard C. Shelby of Alabama, the senior Republican on the banking committee.

Tony Fratto, a spokesman for the White House, said the administration still needed to review the specific language in the bill. But, he said: “We appreciate and encourage the efforts to create a strong, independent regulator” for the government-sponsored companies. “We’ll look forward to seeing the details of the bill,” he added, “especially provisions to expand programs of the Federal Housing Administration.”

A spokesman for Mr. Shelby said the senator was “optimistic that the White House will support what we’re doing.”

In a statement, Mr. Shelby said: “My primary consideration during negotiations on this package has been to protect the American taxpayer, and I believe we’ve made significant progress toward that goal on each component.”

Mr. Shelby had been particularly intent on tightening regulation of Fannie Mae and Freddie Mac, and the deal with Mr. Dodd would create a new Federal Housing Finance Agency. The agency would oversee the companies, which are private but are virtually assured of government assistance should they experience financial difficulty.

The regulator would be empowered to order an increase in capital in the event that the “safety and soundness” of the institutions were somehow at risk. In addition, the bill would set a new limit on so-called conforming loans, up to about $550,000 in the most expensive markets. The current conforming loan limit is $417,000, but was raised temporarily to $729,250 in the most expensive housing markets under the economic stimulus plan approved by Congress and signed by the president in February.