President Barack Obama on Tuesday announced a cut in fees on many government-backed mortgages that he said could help millions of homeowners refinance, part of an election-year push to boost the shaky housing market.

Under the plan, a typical borrower with a loan backed by the Federal Housing Administration could save a thousand dollars a year by refinancing into a new FHA loan, the White House said. The fee reductions would be on top of any savings from a lower interest rate.

Two million to three million borrowers would be eligible, although the White House said participation would more likely number in the hundreds of thousands.

The step is the latest in a series by the Obama administration to aid a depressed U.S. housing market and homeowners threatened by a rising tide of foreclosures. About 11.1 million Americans now owe more than their homes are worth.

I'm not one of those people who believe that we just sit by and wait for the housing market to hit bottom, Obama said at a news conference. There are real things we can do right now that would make a substantial difference in the lives of innocent, responsible homeowners.

Obama, who faces re-election in November, introduced the cut in mortgage fees alongside efforts to compensate members of the military who may have been wrongfully foreclosed.

The lower loans fees being put in place would be available to borrowers seeking a new loan through FHA's streamlined refinancing program, and even borrowers who owe more on their mortgage than their house is worth would be eligible.

Under the streamlined program, borrowers must be current on their payments and income verifications and appraisals are waived. The reduced fees announced today would be available to borrowers who are refinancing loans taken out before June 1, 2009.

Of the 5.4 million 30-year fixed-rate mortgages the FHA backs, 3.2 million would not be eligible because they were issued after the June 1, 2009 cut off date, according to Mahesh Swaminathan, an analyst at Credit Suisse Group AG.

This should be broadly positive for housing and the economy by reducing foreclosures and freeing up income for consumers to spend on other goods and services, Jaret Seiberg, senior policy analyst with Guggenheim Securities, wrote in a note to clients.

The biggest banks, such as Wells Fargo & Co. , Bank of America Corp and JPMorgan Chase & Co. , are likely to see an uptick in refinancing volume, which could mean increased income from fees related to FHA mortgages, he wrote.

While mortgage rates are at historic lows around 4 percent, many Americans lack the equity to refinance. Others are locked out by tight credit conditions.

Obama has announced several changes to the administration's housing policies this year to help borrowers, including an expansion of an existing mortgage relief program that had failed to reach as many homeowners as hoped.

The latest plan, which does not need congressional approval, reduces the cost of up-front FHA mortgage insurance premiums to 0.01 percent from 1 percent of a borrower's loan balance. It also cuts the annual fee for these loans in half to 0.55 percent.

Many FHA borrowers have found refinancing prohibitive in recent years because of increased insurance premiums. The administration has been raising fees for FHA loans to shore up the agency's dwindling capital and shrink its footprint in the market. The FHA backs about a third of all new mortgages.

(Reporting by Margaret Chadbourn; Editing by Andrew Hay)