Fannie Mae’s D.C. headquarters. (J. David Ake/Associated Press)

The chief executives of Fannie Mae and Freddie Mac could collect up to $4 million a year in pay as a result of new government rules that ease restrictions on the leaders’ compensation six years after the mortgage finance giants received massive bailouts to cover losses suffered during the housing bust.

New filings with the Securities and Exchange Commission detail the pay package for Fannie Mae CEO Timothy Mayopoulos and for Freddie Mac CEO Donald Layton.

Both are eligible to receive a base salary of $750,000, deferred salary worth $2.05 million and deferred salary based on performance of $1.2 million. The companies declined comment beyond what they said in filings outlining the new compensation levels.

Neither executive was in place in 2008 when the government took over Fannie Mae, based in the District, and Freddie Mac, based in McLean, Va. At the time, the finance giants were teetering, having suffered huge losses by guaranteeing risky mortgages leading up to the housing downturn.

Under terms outlined by the government’s bailout plan, compensation for the chief executives was limited to $600,000. The decision to raise the limit was approved by the Federal Housing Finance Agency, which oversees the companies.

“The plan defers significant compensation to ensure retention, is based on performance, does not include a bonus and is consistent with FHFA’s statutory responsibilities to ensure safety and soundness and a liquid national housing finance market,” Mel Watt, head of the FHFA, said in a statement.

The $4 million amount is also below the typical compensation that 75 percent of executives in comparable companies make, he said.

The two government-controlled mortgage giants are profitable again thanks to an improving housing market, and the enterprises have paid back Treasury funds used to bail them out.

Still, the White House and lawmakers on both sides of the aisle sharply criticized the change.

Sen. Mark Warner (D-Va.), a member of the Senate Banking Committee, said the raises suggested a return to “business as usual” at a time when lawmakers are trying to recast the federal role in mortgage finance.

“These extraordinary pay raises fly in the face of the legislative intent,” he said.

In a statement, Sen. Bob Corker (R-Tenn.) said he understood the agency’s rationale to increase compensation as a way to retain talent. But the decision could drive the mortgage finance giants back to the “failed” model of private gains and public losses, he said.

Both Warner and Corker have sponsored legislation to reform housing finance.