WASHINGTON » Fannie Mae is asking for less money from the government, a sign that the cost to taxpayers for bailing out the mortgage giant could be billions lower than once thought.

The government-controlled mortgage buyer said yesterday it has now set aside enough money to cover the majority of losses stemming from bad loans made from 2005 through 2008.

It requested $1.5 billion in additional taxpayer aid after posting the best quarterly results since the company was put under federal control in September 2008. It was also the smallest quarterly request for assistance since November 2008.

Fannie Mae said yesterday it lost $3.13 billion last quarter, which takes into account $1.9 billion in dividends paid to the Treasury Department. The company lost $15.2 billion in the year-ago quarter.