Under the Bachus proposal, which the panel approved on a 52-4 bipartisan vote, the top executives could have earned no more than $218,978 in compensation and would receive no bonus pay.
The legislation hasn't been considered on the House floor yet.
"The reports that surfaced recently that corrective action may finally be taken by regulators to stop these lavish pay packages in the future are welcome, but long overdue," Bachus said.
Both chief executives — Fannie Mae's Michael Williams who earned $5.6 million last year and Freddie Mac's Charles Haldeman Jr., who took home $5.4 million from base annual salaries of $900,000 — have announced they will leave their respective firms this year.
Fannie and Freddie said late last year that would give out $12.8 million in bonuses to the top executives.
“The taxpayer-funded bailout of Fannie Mae and Freddie Mac is the biggest bailout in history," Bachus said.
"Forcing taxpayers to fund these excessive salaries and bonuses just adds insult to injury,” he said.
Congressional Republicans and Democrats are calling for an overhaul of the two government-sponsored enterprises. The White House proposed three options last year and asked Congress to reach an agreement before the end of 2012 but any decisions seem unlikely this year.
Salary considerations could range between $250,000 to $500,000, although the Federal Housing Finance Agency, the overseer of the two firms, hasn't made any decisions on how much top executives would make.
In November hearings, Edward DeMarco, the FHFA's acting director, told lawmakers that it would be nearly impossible to attract qualified employees with federal-government-level pay.
The top executives at Fannie Mae and Freddie Mac have said their employees deserved the millions of dollars in bonuses they were awarded.
The executives said they understand why people are upset about the payouts at the mortgage giants, which were brought under federal control in 2008.
But the executives said the sweeteners in the pay packages are necessary to help protect taxpayers from the losses that would result if Fannie and Freddie failed to retain their best workers.
DeMarco told a Senate panel during those November hearings that his agency would look into reducing pay.
The executives pointed out that compensation for their workers has fallen by about 40 percent from before Fannie and Freddie came under federal conservatorship, and said there are difficulties in working for the entities, given their uncertain future, scrutinized position and lagging pay compared to other employment options.
Since their bailout Fannie and Freddie have received $170 billion in taxpayer dollars.