Aiming to fight off market fears of insolvency, Fannie Mae and Freddie Mac issued statements late Friday insisting they have adequate capital.

The statements from the government-sponsored mortgage giants were released minutes after the Federal Reserve denied having discussions with the companies on allowing them access to the central bank's emergency discount window.

"The Fed is following the situation closely," a spokesperson from the central bank told FOX Business. The statement conflicted earlier reports indicating Federal Reserve Chairman Ben Bernanke told Freddie that it and Fannie Mae would have access to the emergency funding. 

The financial health of the two government-sponsored entities was the focal point of a tumultuous day on Wall Street.

Fannie insisted in a separate statement that its capital level "is substantially above" mandated levels. The company also said it raised $7.4 billion of additional capital in May, bringing its total to $14 billion since November 2007.

"In fact, we have more core capital, and a higher surplus over our regulatory requirement, than at any time in this company's history," said Chuck Greener, senior vice president of Fannie.

Freddie said in an e-mail that it is under no mandate to raise capital in the near-term, according to Reuters. The company also reportedly said it has several options to manage its capital, such as cutting its dividend. Freddie said it is "not on the threshold of conservatorship," refuting an earlier media report of a government takeover. 

The liquidity statements are very significant as the market has begun to fear that Fannie and Freddie could fail. The fears have grown even as federal officials, and the companies themselves, have insisted the mortgage giants are adequately capitalized. 

The New York Times reported in its Friday edition that the government is considering a takeover of both Fannie and Freddie if their financial situations deteriorate. Such a scenario would leave shareholders with little to no value.

Many on Wall Street believe Fannie and Freddie are too big and too important to the housing market to be allowed to fail. The government-sponsored companies own or back more than $5 trillion of U.S. mortgages. A failure would likely do very serious damage to the nation's already slumping housing market.