The lawsuit seeks to recover hundreds of millions of dollars in insurance claims the government paid when homeowners defaulted on mortgages, plus punitive damages.

The bank allegedly made substantial profits between 2007 and 2009 from the resale of the risky mortgages, leaving the government to foot the bill for loans in default.

The lawsuit said the bank carried out the fraud through its subsidiary, MortgageIT, which employed more than 2,000 people at branches in all 50 states. Deutsche acquired MortgageIT in 2007.

US Attorney Preet Bharara said the bank “repeatedly and brazenly’’ engaged in a pattern of reckless lending with mortgages “that were really ticking time bombs’’ — sometimes failing to verify that a mortgage applicant had a job.

“In fact, they often seemed to treat red flags as if they were green lights,’’ he said.

He said the government found no evidence of the criminal intent necessary to take the case beyond a civil lawsuit.

Deutsche said it was reviewing the complaint but called the allegations unreasonable and unfair.

Nearly 90 percent of the activity that is described in the lawsuit occurred before Deutsche Bank acquired MortgageIT, a spokeswoman said.

Since last fall, federal regulators and attorneys general of all 50 states have been investigating lenders accused of cutting corners and using flawed documents to foreclose on many homeowners.

In some cases, employees of financial institutions engaged in so-called robo-signing — approving documents in foreclosures without actually reading them. Foreclosure-fraud class-action lawsuits against major banks nationwide are piling up.

Bharara said it “would not be a fantastical stretch to think we are looking at other lending institutions, as well.’’

The lawsuit against Deutsche seeks to recover more than $386 million paid out in Federal Housing Administration insurance claims and related costs arising out of MortgageIT’s approval of more than 3,100 mortgages.

The lawsuit said Deutsche Bank and MortgageIT failed to comply with Department of Housing and Urban Development regulations regarding required quality control procedures, and then lied about their purported compliance.

The government said the quality control violations were egregious, including the failure to review all early payment defaults and to implement minimal quality controls.