WASHINGTON — The federal government today ordered 16 of the nation’s largest mortgage lenders and servicers to reimburse homeowners who were improperly foreclosed upon.

Government regulators also directed the financial firms to hire auditors to determine how many homeowners could have avoided foreclosure in 2009 and 2010.

Citibank, Bank of America, JPMorgan Chase and Wells Fargo, the nation’s four largest banks, were among the financial firms cited in the joint report by the Federal Reserve, Office of Thrift Supervision and Office of the Comptroller of the Currency.

In the four years since the housing bust, about 5 million homes have been foreclosed upon. About 2.4 million primary mortgages were in foreclosure at the end of last year. Another 2 million were 90 days or more past due, putting them at serious risk of foreclosure.

Critics, including Democratic lawmakers in Congress, say the order is too lenient on the lenders. House Democrats introduced legislation today that would require lenders to perform a series of steps, including an appeals process, before starting foreclosures.

The other lenders and service providers cited by the agencies include: Ally Financial Inc., Aurora Bank, EverBank, HSBC, MetLife Bank, OneWest Bank, PNC, Sovereign Bank, SunTrust Banks, U.S. Bank, Lender Processing Services and MERSCORP.