NEW YORK — Bank of America 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 less 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, JPMorgan Chase and Wells Fargo. Some estimates ran as high as $10 billion.

“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.

The claims stem from mortgages sold to Fannie and Freddie by former mortgage giant Countrywide Financial, which Bank of America bought in 2008.