Bank of America Corp. Chief Executive Officer Brian T. Moynihan said efforts to prevent foreclosures are failing frequently, with more than half of borrowers in some categories defaulting a second time.

“We’re reaching a point where some customers will be dealing with the reality that despite the myriad programs and the best efforts of everyone in this room, and of our teammates working with these customers, foreclosure may be unavoidable,” Moynihan said today during a speech to state attorneys general in Charlotte, North Carolina.

Bank of America and other mortgage servicers are being probed by a task force of 50 state attorneys general over the way they foreclosed on overdue homeowners. The regulators have suggested a $20 billion penalty for the industry and principal reductions for some owners whose debt is greater than the value of their home.

Bank CEOs including Moynihan, who runs the biggest U.S. mortgage servicer, and JPMorgan Chase & Co.’s Jamie Dimon have rejected principal reductions as unfair.

“We do not see broad-based principal reduction as a sound policy decision for America,” said Moynihan, 51, according to the prepared text of his speech.

“It’s hard to see how we could justify reducing principal for many delinquent customers who represent a small portion of borrowers, but not for the vast majority of our customers who have stayed current on their loans.”

The servicers have signed agreements with regulators including the Federal Reserve and Office of Thrift Supervision to improve foreclosure practices, two people with knowledge of the deals said last week. They are the first sanctions to arise from last year’s probe into so-called robo-signing, in which mortgage firms and their contractors vouched for thousands of foreclosure documents without verifying their accuracy.

Bank of America fell 7 cents, or 0.5 percent, to $13.42 at 1:06 p.m. in New York Stock Exchange composite trading. The shares are little changed this year.