WASHINGTON — Government-controlled mortgage buyers Fannie Mae and Freddie Mac cut their losses in the final three months of last year. But they are asking for more money from taxpayers as the real estate market braces for what could be a new wave of mortgage defaults.

Fannie Mae on Thursday posted a loss of $2.1 billion for the October-December quarter, after payment of $2.15 billion in dividends to preferred stock that is mostly owned by the federal government. It has requested an additional $2.6 billion in federal aid, slightly more than the $2.5 billion it sought in the previous quarter. Freddie Mac managed a $1.7 billion loss for the final quarter of last year, after the payment of $1.6 billion in preferred dividends. It has asked for an additional $500 million in federal aid — up from the $100 million it sought in the July-September quarter of 2010.

Both companies narrowed their losses from 2009’s final quarter, when Fannie Mae reported a shortfall of $16.3 billion and Freddie Mac lost $7.8 billion. Fannie Mae also reported a $21.7 billion loss for all of 2010, narrowed from a loss of $74.4 billion the year before.

Freddie Mac’s loss last year was $19.8 billion, compared with a $25.7 billion loss in 2009.

“The good news is that their losses are shrinking,” said Anthony Sanders, a professor of real estate finance at George Mason University.

The bad news? “This is just the calm before the storm. ... They’re going to be hit with some staggering losses,” Sanders said.

The continuing erosion of the housing market, and a coming wave of foreclosures that had been put on hold because of widespread problems with lenders’ documents, could bring significant losses for Fannie and Freddie in the near future, Sanders said.