The House Republicans offered five goals to guide the overhaul of Fannie Mae (FNM.N) and Freddie Mac (FRE.N), which were chartered by Congress with a mandate to provide liquidity to the U.S. housing market but are privately held by shareholders. The goals include reestablishing a housing finance market in which private capital is the primary source of mortgage financing.

The lawmakers put forward 10 principles, among them winding down Fannie Mae and Freddie Mac and cutting their mortgage portfolio holdings by 25 percent a year over four years.

"It is time to deal with bailed-out companies, which were at the center of the mortgage market meltdown that caused the financial crisis and have cost taxpayers hundreds of billions of dollars," said Representative Spencer Bachus, an Alabama Republican, and ranking member of the House Financial Services Committee.

The committee, chaired by Representative Barney Frank, a Massachusetts Democrat, is to hold a hearing on the future of housing finance on Tuesday.

In an interview on CNBC on Friday, Frank said the mortgage finance firms needed restructuring because the partially public, partially private "hybrid" was not workable.

"We made a mistake -- not me, I wasn't there when it was enacted but we helped perpetuate it -- setting up Fannie Mae and Freddie Mac as hybrids," he said.

"They were private shareholder corporations with a need to make a profit but they were also given this public mandate. That worked well when everything was doing fine, but when things got bad it wasn't working well," Frank added.

Treasury Secretary Timothy Geithner will testify and is expected to offer broad thoughts on how the role of Fannie Mae and Freddie Mac should change.

Earlier this week, Geithner told lawmakers "fundamental reform" of the government's role in the housing finance market is needed, but he said it will be next year before the Obama administration has any proposals ready for Congress.

Fannie Mae and Freddie Mac in September 2008 were seized by the U.S. government to quell what had been a year-long credit market crisis that had helped push many economies toward recession.

In testimony on Wednesday, Federal Reserve Chairman Ben Bernanke urged Congress to come up with a new way of financing homes.

"My assumption is that sometime soon, I'd hope soon, that the Congress will reform Fannie and Freddie, perhaps break them up, perhaps make them officially governmental," Bernanke told the House Financial Services Committee.