But they face fierce resistance from lawmakers worried about cutting jobs during a recession, especially those whose states face job losses if production of the Lockheed Martin-built F-22 ends.
Lockheed Martin says there are 25,000 jobs nationwide directly dependent on the F-22 and thousands of others in support of the programme.
The bill, however, poses other problems for Obama. Lawmakers elected to retain funding to develop an alternative engine for the F-35 Lightning II, a multi-role fighter that has yet to go into full production. They're estimated to cost about $80 million each.
The House also approved funding for a new presidential helicopter.
Obama has said he will veto a bill that provides money for both the helicopter and the F-35 alternative engine.
The Senate has yet to take up the defence budget legislation.