Government-controlled mortgage buyer Fannie Mae is asking for $2.5 billion in additional federal aid after posting a narrower loss in the third quarter.

Fannie Mae also said Friday it was likely that the market disarray and suspension of foreclosures due to big lenders’ problems with flawed documents will have a negative impact on the delinquency rates of its loans, its expenses and foreclosure timelines. However, the company said, “we cannot yet predict the extent of its impact.”

Fannie Mae said Friday it lost $3.46 billion, or 61 cents a share, in the July-September quarter. That takes into account $2.1 billion in dividend payments to the Treasury Department. It compares with a loss of $19.8 billion, or $3.47 a share, in the third quarter of 2009.

The government rescued Washington-based Fannie Mae and sibling company Freddie Mac about two years ago and it estimates that will cost taxpayers up to $259 billion. That’s nearly twice the $133.4 billion Fannie and Freddie are in line to receive from taxpayers so far and would make it the most expensive bailout of the financial crisis.

The $2.5 billion in additional aid that Fannie is asking for compares with a request for $1.5 billion in the second quarter.

Fannie and Freddie together have repaid $16.7 billion as dividends to the Treasury Department.

Fannie’s chief executive said Friday the latest results reflect ongoing efforts to contain losses from the high-risk mortgages it bought from 2005 to 2008 and to build up new, more profitable loan business with tighter lending standards.

McLean, Va.-based Freddie Mac reported Wednesday that it managed a narrower loss of $4.1 billion for the third quarter and asked for an additional $100 million in federal aid — far less than the $1.8 billion it sought in the second quarter.

But neither Fannie nor Freddie are out of the woods yet.

The two mortgage giants have been hit by massive losses on risky mortgages purchased from 2005 through 2008. The companies have tightened their lending standards after those loans started to go bad, and default rates on new loans are far lower.

The housing market, however, remains a huge challenge. High unemployment, tepid economic growth, tight credit and uncertainty about home prices have kept people from buying.

Add to that the uncertainty stemming from allegations that big lenders used flawed foreclosure documents to seize millions of homes, a controversy that could put added scrutiny on Fannie and Freddie and bring fresh losses for them.

Fannie and Freddie used some of the same law firms that are accused of processing foreclosure files with flawed documents. They are revoking thousands of foreclosure cases from one Florida law firm which is under investigation for falsifying documents used to complete foreclosures.

Several major banks have been accused of similar conduct. If the banks can’t resolve their foreclosure problems and are barred from seizing many homes, Fannie and Freddie could absorb huge losses on loans they own or guarantee. That’s because they would no longer be able to recover anything on loans that have gone bad.

Fannie and Freddie buy up home loans from lenders, bundle them together into securities with a guarantee against default and sell them to investors worldwide. They own or guarantee about half of all U.S. mortgages, or nearly 31 million home loans worth more than $5 trillion.

Fannie Mae reported its earnings three days after midterm elections in which criticism of the government’s financial bailouts had figured prominently in many races. Fannie and Freddie have many critics, especially among Republican lawmakers whose party gained control of the House in Tuesday’s elections.

Over the next year, lawmakers plan to review the nation’s mortgage-lending system and consider a potential replacement for Fannie and Freddie. The financial overhaul signed by President Barack Obama in July didn’t address that issue, despite protests from Republicans that it was incomplete without such a plan.

An analysis issued Thursday by Standard & Poor’s found the total eventual cost to taxpayers of rescuing Fannie and Freddie and funding new entities to replace them could reach $685 billion.