Between 1999 and 2009, the bank’s subsidiary, MortgageIT, got backing from the Federal Housing Administration for more than 39,000 loans worth more than $5 billion. In exchange, the firm was required to ensure that its lending met federal standards.

But, prosecutors say, the bankers “never held up their end of the bargain.”

“Borrower after borrower defaulted — often within just months of closing — because those loans were doomed to fail,” Preet Bharara, U.S. attorney for the Southern District of New York, said at a news conference.

As of February, the government had paid more than $386 million in insurance claims and other costs for loans approved by the bank that went bad. The complaint says the government expects to pay hundreds of millions of dollars more to cover bad loans underwritten by the bank.

Deutsche Bank responded saying that “close to 90 percent” of the activity covered in the complaint happened before it acquired MortgageIT in 2007. At the time, MortgageIT had been an approved FHA lender for nearly a decade, the bank said in a statement.

“We believe the claims against MortgageIT and Deutsche Bank are unreasonable and unfair, and we intend to defend against the action vigorously,” Deutsche Bank said.

The complaint paints a picture of a bank taking short cuts.

When an outside auditor found serious problems at MortgageIT, the concerns were “literally stuffed in a closet and left unread and unopened,” the complaint said. MortagageIT also failed to closely watch its own lending practices. At one point it reassigned its lone staff member in charge of auditing FHA-insured loans to churn out more mortgages, the complaint alleges. When the government found evidence the bank was violating requirements to check for the quality of the mortgages, MortgageIT promised to fix the problems and then did nothing.

The banks also repeatedly claimed eligibility for FHA loans that did not meet government rules, prosecutors said.

“While they promised to select qualified mortgages to be insured, they repeatedly abused that public trust by brushing aside the rules, lying about the quality of their underwriting operation, and passing on the costs of the inevitable hundreds of millions of dollars of defaults to the government,” said Bharara, whose office is also pursuing a major insider trading ring. “It wasn’t their problem anymore. The government held all the risks and, ultimately, was left holding the bag.”

The bank was also singled out in a report released last month by a U.S. Senate panel that investigated the causes of the financial crisis. That inquiry charged Deutsche Bank and Goldman Sachs with selling complex financial products filled with loans that traders at the banks viewed as being worthless.

“As alleged, MortgageIT and Deutsche Bank ignored every type of red flag and breached every duty of due diligence before underwriting thousands of federally insured mortgages,” Bharara said. “While the homes the defendants issued loans for may have been built on solid ground, the defendants’ lending practices were built on quicksand.”