CORRECTED - UPDATE 2-Democrat says abolish Freddie, Fannie-FOX

(Corrects ownership status of companies in fifth paragraph)

*Rep. Frank suggests ending "hybrid" financing

*Frank says guarantees should be self-financed

*Rethink homeownership policy, Frank says

By JoAnne Allen

WASHINGTON, Aug 17 (Reuters) - Fannie Mae and Freddie Mac should be abolished rather than reformed as part of the Obama administration's planned overhaul of the government's role in housing finance, Rep. Barney Frank, chairman of the House Financial Services committee, said on Tuesday.

"They should be abolished," Frank said in an interview on Fox Business, when asked whether the mortgage giants should be elements in housing market reform. "They only question is what do you put in their place," Frank said.

The Federal Housing Administration should be fully self-financing and Freddie and Fannie should be replaced with a new mechanism to help subsidize housing, Frank said in the interview.

"There is no more hybrid private-public," the Massachusetts Democrat suggested. "If we want to subsidize housing then we could do it upfront and let the budget be clear about that."

Fannie Mae and Freddie Mac were government-sponsored enterprises, privately owned companies supported by the government, until the Bush administration took control of the companies in 2008 to save them from collapse.

Frank said that he does believe the federal government should have a role in building affordable rental housing but thinks money should go toward projects by private developers.

On the question of whether the government should still provide some guarantees in the mortgage market, Frank said: "If we have it (guarantees), it has to be self-financed by the people who are benefiting."

Frank commented after Treasury Secretary Timothy Geithner convened a Washington conference of housing industry leaders to hear ideas about reforms for the $10.7 trillion mortgage market.

The firms' pursuit of growth and profits helped precipitate the financial crisis of 2007-2009, but their vast resources also helped minimize its impact.

Together, Fannie and Freddie and the Federal Housing Administration now back 90 percent of new U.S. home mortgages.

Fannie and Freddie have received $150 billion in taxpayer bailout money.

In the Fox Business interview, Frank also was critical of public policy that promoted homeownership at any cost. He also said the federal government should not be a "backstop" in guaranteeing mortgages.

"There were people in this society who for economic and, frankly, social reasons can't and shouldn't be homeowners," Frank said. "I think we should, particularly, stop this assumption that you put everybody into homeownership."

"Public policy has been too much to try to push people into homeownership." (Reporting by Joanne Allen; editing by Sofina Mirza-Reid and Carol Bishopric)