Sponsored by conservative Rep. Todd Akin, R-Mo., the so-called "court stripping" bill would remove cases involving the pledge to the U.S. flag from federal court jurisdiction.
It is a response to a recent case in which the constitutionality of the phase "under God" in the pledge was challenged. Congress added the phrase in the 1950s in response to the perceived threat of communism to U.S. interests.
The 9th U.S. Circuit Court of Appeals ruled in 2002 the phrase violated the constitutional separation of church and state, but the Supreme Court struck down the decisions in June on technical grounds.
But the high court did not not rule on the constitutional issues involved, leaving open the chance for another legal challenge.
Proponents of the move say it is needed to rein in "activist" judges overstepping the bounds of the judicial branch, while critics contend it violates established legal precedent.
While the House approved the bill, it is not likely to become law anytime soon as it is not expected to be taken up in the Senate this year.