By Corbett B. Daly

WASHINGTON (Reuters) - A bill to create a new market for financing mortgages that would help wean the $10.6 trillion mortgage market off government support advanced in the House of Representatives on Tuesday.

The House Financial Services Subcommittee on Capital Markets and Government Sponsored Enterprises approved the legislation on a voice vote.

The bill, which the White House supports, would have to be approved by the full committee, the full House and the Senate before being sent to President Barack Obama for his signature into law.

The bill aims to establish a market for covered bonds, which are securities issued by banks and backed by pools of loans.

The loans underlying the covered bonds would remain on the issuer's balance sheet. That is different from the current U.S. mortgage system, in which lenders sell many of the loans they make to government-sponsored Fannie Mae <FNMA.OB> and Freddie Mac <FMCC.OB>, which then repackage them as securities for investors.

The panel's chairman, New Jersey Republican Representative Scott Garrett, hopes to reduce the role of Fannie Mae and Freddie Mac with a covered bond market.

Senator Charles Schumer, a New York Democrat, said in March he was considering introducing a version of Garrett's bill in the Senate.

Representative Carolyn Maloney, a New York Democrat, backed Garrett's bill as one way to help the U.S. mortgage market on the margins, though she cautioned that it is not a panacea.

"Why not give it a chance?" Maloney said, adding that she considers covered bonds "a strong tool we could use to help ... our housing market rebound."

The government seized Fannie Mae and Freddie Mac in 2008 as losses on the loans they held spiraled.

The government, through Fannie Mae, Freddie Mac and the Federal Housing Administration, now backs almost nine in 10 new mortgages.

In Europe, covered bonds have long been in use. But they have failed to catch on in the United States.

In a covered bond system, banks can borrow against the value of the underlying mortgages to obtain fresh capital to extend further loans. The bond investors have the right to those underlying assets in the case of a bank default.

The Federal Deposit Insurance Corporation has warned that a covered bond system could put its bank deposit insurance fund at increased risk for losses because the investors would have seniority over the agency in the event of default.

Treasury Secretary Timothy Geithner has said the FDIC's concerns are legitimate and would have to be worked out.

"For this to work, you would be putting the taxpayer in some sense behind private investors, and that has its own consequences, but that is something we can work through and I think it can play a greater role in our system," Geithner said in March.

The White House and Congress are in the midst of a major policy debate on how to overhaul the finance system for buying U.S. homes, which collapsed in 2008.

The Obama administration in February announced several steps to make government-backed mortgages more expensive in a bid to lure private capital back to the mortgage market.

It also announced plans to phase-out Fannie Mae and Freddie Mac over time and presented Congress with three options for replacing them long-term.

(Reporting by Corbett B. Daly, Editing by Dan Grebler)