New York ? Bank of America Corp. reached a $2.8 billion settlement with Fannie Mae and Freddie Mac over claims that one of its businesses sold bad mortgages. The payment is far lower than analysts expected and removes some uncertainty that has hovered over the bank.

The settlement is the biggest yet involving banks and the two government-backed mortgage giants, which continue to suffer huge losses from the collapse of the housing market. Analysts and investors have been waiting to see how hard a line Fannie and Freddie would take with big mortgage lenders such as Citigroup Inc., JPMorgan Chase & Co. and Wells Fargo & Co. Some estimates ran as high as $10 billion for a Bank of America settlement.

“The government gave Bank of America a very attractive deal,” said Christopher Whalen, managing director of Institutional Risk Analytics.

Bank stocks rallied on the news, with Bank of America up more than 6 percent and Wells Fargo up 2 percent. Other settlements are likely soon.

The claims stem from mortgages sold to Fannie and Freddie by former mortgage giant Countrywide Financial, which Bank of America bought in 2008. The two government-backed agencies buy mortgages from lenders and resell them to investors. They want banks to buy back mortgages that had incorrect information about the income and other qualifications of borrowers. During the housing boom, lenders such as Countrywide routinely gave mortgages to people who ultimately couldn’t afford them. This lit the fuse for the financial meltdown in 2008. Most of the mortgages that Fannie and Freddie want to sell back to the banks are in default.

By removing this as an issue, Bank of America CEO Brian Moynihan hopes investors will buy his message of focusing on customers and building its traditional banking business. But Bank of America has several big challenges remaining. Last fall, the bank was accused of using faulty documents to foreclose on thousands of homeowners. All 50 state attorneys general have launched investigations into the foreclosure practices of Bank of America and other banks. Bank of America also faces lawsuits from other investors who are trying to recoup losses from mortgages they say contained faulty information.