The Justice Department filed a lawsuit Thursday against Quicken Loans, the nation’s third-largest mortgage lender, contending that it made hundreds of improper loans through the Federal Housing Administration lending program, costing the agency millions of dollars.

The F.H.A. does not make loans itself, but insures them. Participating lenders, including Quicken, which makes more F.H.A. loans than any other institution, have the authority to originate, underwrite and certify mortgages covered by F.H.A. insurance. Under the program, if the borrower later defaults, the holder of the loan can file an insurance claim to cover losses.

The Justice Department contends that from September 2007 through December 2011, Quicken knowingly submitted claims — or caused the submission of claims — on hundreds of bad loans, and encouraged an underwriting process in which employees disregarded the program rules and falsely certified that loans met the requirements.