The legislation, a priority of social conservatives, passed 260-167. It now goes to the Senate where its future is uncertain.
The Pledge of Allegiance is the oath said aloud while facing the U.S. flag, routinely recited by school children and immigrants when they are sworn in as citizens.
"We should not and cannot rewrite history to ignore our spiritual heritage," said Rep. Zach Wamp. "It surrounds us. It cries out for our country to honor God."
The idea behind the legislation is that Republicans don't trust the Supreme Court and think it might someday rule that "under God" needs to be removed from the pledge that schoolkids recite, CBS Radio News correspondent Bob Fuss reports.
Opponents said the legislation, which would bar federal courts from ruling on the constitutional validity of the pledge, would undercut judicial independence and would deny access to federal courts to religious minorities seeking to defend their rights.
"We are making an all-out assault on the Constitution of the United States which, thank God, will fail," said Minority Leader Nancy Pelosi.
The pledge bill would deny jurisdiction to federal courts, and appellate jurisdiction to the Supreme Court, to decide questions pertaining to the interpretation or constitutionality of the pledge. State courts could still decide whether the pledge is valid within the state.
The legislation grew out of a 2002 ruling by the 9th U.S. Circuit Court of Appeals that the pledge is unconstitutional when recited in public schools.
The Supreme Court in 2004 reversed that decision on a technicality, saying atheist Michael Newdow did not have legal standing to sue on behalf of his daughter because the mother had custody of the child. Newdow has since revived the case and last year a U.S. District Judge ruled in his favor.
Newdow, an attorney and medical doctor, said in an interview that he hoped the bill would pass to expose the aims of its supporters. "They're willing to ruin this country so they can keep their God in our country. I love the fact that they are having a vote." He said he expected a final ruling in his case in about a year.
Supporters argued that the "under God" phrase, added to the pledge in 1954, was intrinsic to U.S. heritage and traditions and must be shielded from unelected judges. "This is an issue that clearly resonates to what we are about as a country," said House Republican Whip Roy Blunt.
Rep. Todd Akin, who sponsored the measure, said that denying a child the right to recite the pledge was a form of censorship. "We believe that there is a God who gives basic rights to all people and it is the job of the government to protect those rights."
Davison Douglas, a professor at the William and Mary School of Law, said constitutional scholars are divided over whether such congressional restrictions on judicial review would pass constitutional muster.
He noted that "past efforts to bar all federal court review of hot-button social issues have consistently failed. Hence, if this bill is enacted, it would be a highly significant landmark in terms of congressional efforts to control the actions of federal courts."
There is a companion Senate bill, but it is unclear whether the Senate will take it up in the current session.