WASHINGTON – The government spelled out Thursday just how much the most expensive rescue of the financial crisis will end up costing taxpayers – as much as $259 billion for mortgage buyers Fannie Mae and Freddie Mac.

That figure would be nearly twice the amount Fannie and Freddie have received so far. To date, the two companies have received $135 billion from taxpayers and have repaid $13 billion to the Treasury Department as dividends.

contrast, the combined bailouts of financial companies and the auto industry have cost taxpayers roughly $50 billion, according to Treasury’s latest projections. And the bailouts of Wall Street banks alone, which sparked public fury, have so far brought taxpayers a $16 billion return.

Fannie and Freddie were battered by losses on loans they backed, once the housing bubble burst and foreclosures soared. The two companies buy home loans from lenders, package them into bonds with a guarantee against default and sell them to investors.

On Thursday, the government provided a broad estimate of the costs of bailing out Fannie and Freddie. The final cost will depend on the direction of home values over the next few years. If prices fall sharply, as some analysts forecast, Fannie and Freddie won’t be able to recover as much money on foreclosures. They would require more taxpayer aid.

The Fannie-Freddie bailout could end up costing taxpayers between $142 billion and $259 billion through 2013, the Federal Housing Finance Agency projected.

The worst-case scenario assumes the economy would fall back into a recession and home prices would sink an additional 24 percent, until early 2012. The best-case scenario assumes home prices remain flat for the next two years.

Thursday’s estimate was the first time the housing agency has released a public estimate of the taxpayer tab. The combined bailout of the two mortgage companies is on track to be the largest of the financial crisis.

The agency’s figures take into account dividends that the agency estimates Fannie and Freddie will end up repaying. The terms of their rescue require them to pay a 10 percent annual dividend to Treasury. That amount is expected to balloon in coming years. Regulators expect Fannie and Freddie to repay an additional $67 billion to $91 billion in dividends over the next three years.

The two mortgage finance companies have been operating under federal control for more than two years.