[Update 1: Adds comments from President Obama]

The Federal Housing Administration will lower refinance premiums, and major mortgage servicers will provide relief to wrongfully foreclosed military members, the White House said.

President Barack Obama detailed the new housing measures in a press conference Tuesday afternoon, as voters in 10 states head to polls in the latest primary battle between Republican presidential candidates.

"This is not something the government by itself can solve," Obama said. "But I'm not one of those people who can sit around and wait for the housing market to hit bottom."

The FHA will cut its initial mortgage premium to 0.01% of the borrower's loan balance from 1% on refinanced loans, and the annual fee to 0.55% from 1.15%. Eligible mortgages include only those originated before June 1, 2009, and insured by the FHA.

Housing and Urban Development Secretary Shaun Donovan acknowledged that cutoff date will leave out some homeowners, but said the majority of those with higher rates will qualify. It matches the requirements of the Home Affordable Refinance Program for Fannie Mae and Freddie Mac mortgages.

"We wanted to try and create as much consistency across the industry as possible," Donovan said during a conference call.

A homeowner with a $175,000 mortgage refinanced at 4% would save an additional $100 in insurance premiums each month, according to the White House.

An estimated 2 million to 3 million homeowners could benefit from the changes, though the Obama administration cautioned it's "always difficult to estimate participation in these programs."

Jaret Seiberg, a policy analyst at Guggenheim Securities, said the lower premiums should reduce foreclosures and free up spending money for consumers. Big banks could also get a boost in fee income related to FHA mortgages, he said.

But the lowered rates could cause prepayments to accelerate on mortgage-backed securities from these loans, Seiberg said.

Military members could also receive compensation for wrongful foreclosures from the major servicers, previously highlighted at the time of the $25 billion mortgage servicing settlement in February. Wrongfully foreclosed service members would get the higher of lost equity and $116,785, or an amount provided through a review by banking regulators.

Tom Perez, Assistant Attorney General in the Justice Department, said it's unclear how many service members were affected, but said "we will certainly be in the thousands." He said servicers failed to get a court order in a majority of these cases.

Major lenders could also pay if service members were charged an interest rate above 6% and they made a valid request for a lower rate dating back to 2008. Mortgage servicers would have to pay at least four times the amount of excess interest payments.

The settlement would also require lenders to approve short sales and not seek deficiency judgments for relocated military members who purchased homes between July 2006 and December 2008 or changed stations after Oct. 1, 2010.

The measures are the latest efforts to help boost the housing market from the White House, including a plan to extend refinancings to loans not backed by Fannie Mae or Freddie Mac. That, unlike Tuesday's measures, requires congressional approval.