The head of Bank of America Corp., the United State's fourth-biggest mortgage lender, said banks would be able to supply a bigger share of funding for home purchases if the standard down payment for buyers was cut to 10 percent from 20 percent.

The vast majority of mortgages are underwritten to strict standards set by the U.S. government or quasi-government entities Fannie Mae and Freddie Mac.

While down payment requirements can vary, they offer fairly little latitude to lenders that do not want to take all the risk themselves. As a result, many prospective homebuyers who cannot come up with a 20 percent down payment are unable to get a loan.

"Our goal - going back to regulatory reform - is should you move the down payment requirement from 20 percent to 10? It wouldn't introduce that much risk but would actually help a lot of mortgages get done," Chief Executive Officer Brian Moynihan told CNBC in an interview Thursday.

Bank of America was the top U.S. mortgage lender ahead of the 2008 mortgage crisis, causing it to face greater losses, both from defaults and litigation, than any other bank. Under Moynihan, who took the helm at the start of 2010, the bank has tightened lending standards and executives regularly use the motto "responsible growth" in public speeches.

Bank of America has ceded market share partly because, unlike peers Wells Fargo and JPMorgan Chase & Co., it does not acquire mortgages from other lenders.