The chief executive officers of Fannie Mae and Freddie Mac may see more than a sixfold increase in their compensation to $4 million in spite of objections from President Barack Obama's administration and some lawmakers.

The Federal Housing Finance Agency, which controls the mortgage giants and has sole authority over their CEOs' pay, allowed Fannie Mae and Freddie Mac to return compensation closer to historic levels. Fannie Mae CEO Timothy J. Mayopoulos, whose pay had been set at $600,000 since 2012, was given a base salary of $750,000, more than $2 million in deferred pay and performance-based awards of as much as $1.2 million, according to a public filing on Wednesday.

Fannie Mae and Freddie Mac, which have operated with explicit U.S. backing since 2008 following the financial crisis, were told earlier this year by the FHFA that they could consider submitting proposals for new pay plans for Mayopoulos and Don Layton, CEO of Freddie Mac. Layton is also eligible for the same package of as much as $4 million, a separate filing Wednesday shows.

White House press secretary Josh Earnest addressed the pay question in May by saying executive compensation at Fannie Mae and Freddie Mac should be treated differently because the mortgage giants "benefit significantly from a backstop that is provided by the taxpayer." Members of the House and Senate have also complained. Senator Mark Warner, a Virginia Democrat, said in a statement Wednesday that the raises signal a return to business as usual and "fly in the face of the legislative intent" to restructure the federal role in mortgage finance.

"Treasury does not support FHFA's new approach to CEO compensation at Fannie Mae and Freddie Mac and urged the agency to reject any increase," Adam Hodge, a Treasury spokesman, said in an e-mailed statement. "Treasury has consistently recommended that existing limits on compensation continue."

Egbert L.J. Perry, chairman of Fannie Mae's board of directors, said in a May statement that the government- controlled mortgage firm needed to "attract and retain the leadership and talent required to keep the company functioning well." Spokesmen for Washington-based Fannie Mae and McLean, Virginia-based Freddie Mac declined to comment on the pay increases.

When the FHFA approved the pay change, it requested that compensation stay below the 25th percentile of CEO pay at similar financial firms, such as Capital One Financial Corp. and U.S. Bancorp. Mayopoulos's $4 million award is "substantially below" that, according to Fannie Mae's filing. His compensation, as well as Layton's, will be pro-rated for 2015.

FHFA Director Mel Watt said in a statement Wednesday that his agency's authorizations for new Fannie Mae and Freddie Mac pay plans are meant to "promote CEO retention, allow reliable succession planning, and ensure the continuity, efficiency and stability" of the companies.

Former Fannie Mae CEO Michael J. Williams made $5.3 million in 2011, before compensation was reduced. Mayopoulos became CEO of Fannie Mae in 2012. Earlier in his career he worked at Bank of America Corp. Layton, a former JPMorgan Chase & Co. executive, was appointed CEO of Freddie Mac in 2012. His predecessor, Charles E. Haldeman, made $3.8 million in 2011.

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