The federal government should have done more to prevent the subprime mortgage crisis, but the problem has been exacerbated by simultaneous spikes in the interest rates on adjustable mortgages and the softening of the housing market, the chairman of the nation’s largest bank regulator said.

Sheila Bair, chairman of the Federal Deposit Insurance Corp., acknowledged the recent jump in foreclosures and loan delinquencies has spurred regulators to work with banks to try to keep borrowers from losing their homes.