WASHINGTON — The House on Tuesday passed a bill that would recognize same-sex marriages at the federal level, with a bipartisan coalition supporting a measure that addresses growing concerns that a conservative Supreme Court could nullify marriage equality.

Forty-seven Republicans joined Democrats in backing the bill, the Respect for Marriage Act, which would codify the federal protections for same-sex couples that were put in place in 2015, when the Supreme Court ruling in Obergefell v. Hodges established same-sex marriage as a right under the 14th Amendment.

It is a direct answer to Justice Clarence Thomas’s concurring opinion in last month’s ruling that overturned federal abortion rights, in which he wrote that Obergefell and similar cases should be reconsidered.

The support among House Republicans, although far from a majority, was remarkable in a party that for decades has made social conservatism a litmus test, and it suggested the beginnings of a shift in Congress that mirrors a broader acceptance of same-sex marriage as settled law.

The party’s leaders split on the bill. The top two Republicans, Representatives Kevin McCarthy of California and Steve Scalise of Louisiana, voted no. But the No. 3 Republican, Representative Elise Stefanik of New York, and Representative Tom Emmer of Minnesota, the G.O.P. campaign committee chairman, were in favor. Representative Liz Cheney of Wyoming also voted for the bill.

Still, more than three quarters of the party opposed the bill, which passed in a vote of 267 to 157.

The measure faces an uncertain path in the evenly divided Senate, where it was not clear if it could draw the support of the 10 Republicans needed to move it forward. But Senator Mitch McConnell, Republican of Kentucky and the minority leader, declined on Tuesday to state a position on the bill.

House Democratic leaders opted to move forward with the bill after the Supreme Court’s decision overturning abortion rights raised worries about the prospect that the justices might revisit cases that affirmed same-sex marriage rights and the right to contraception. The debate in Congress thrust the issue into the midterm election campaign, where Democrats are eager to draw a distinction between their party’s support for L.G.B.T.Q. rights and opposition by many Republicans.

In the Senate, Chuck Schumer, Democrat of New York and the majority leader, did not commit to bringing up the measure but said he was “going to look at everything that we can do to deal with these issues” following the court’s decision overturning abortion rights in Dobbs v. Jackson Women’s Health Organization.

“Let’s face it: This is a MAGA Supreme Court — a MAGA, right-wing extremist Supreme Court — very, very far away from not only where the average American is, but even the average Republican,” Mr. Schumer said.

Justice Samuel A. Alito Jr., who wrote the court’s decision in Dobbs, said the ruling should not be read as affecting issues other than abortion. But Justice Thomas’s concurrence suggested otherwise, and Justice Alito has suggested before that Obergefell should be revisited, arguing that it invented a right with no basis in the text of the Constitution.

Over the weekend, Senator Ted Cruz, Republican of Texas, said he agreed, asserting in an interview for his podcast that Obergefell and Roe v. Wade had been wrongly decided and that both had “ignored two centuries of our nation’s history.” But he added that overturning the same-sex marriage ruling, which he called “clearly wrong,” could be disruptive and would be unlikely.

“You’ve got a ton of people who have entered into gay marriages, and it would be more than a little chaotic for the court to do something that somehow disrupted those marriages that have been entered into in accordance with the law,” Mr. Cruz said.

The legislation passed on Tuesday would repeal the Defense of Marriage Act of 1996, which defined a marriage as the union between a man and a woman, a law that was struck down by the court but has remained on the books. The legislation would mandate that the federal government recognize a marriage if it was valid in the state where it was performed, which would address the patchwork of differing state laws. That would protect same-sex marriages in the roughly 30 states that currently prohibit them, should the court overturn Obergefell.

The bill also would provide additional legal protections to same-sex couples, such as giving the attorney general the authority to pursue enforcement actions and ensuring that all states recognize public acts, records and judicial proceedings for out-of-state marriages.

“Today, we take an important step towards protecting the many families and children who rely on the rights and privileges underpinned by the constitutional guarantee of marriage equality,” Representative Jerrold Nadler, Democrat of New York and the chairman of the Judiciary Committee, said in a statement. “The Respect for Marriage Act will further add stability and certainty for these children and families.”

The White House issued a statement on Tuesday in support of the bill, a version of which is co-sponsored by Senator Susan Collins, Republican of Maine.

The House vote reflected a shift among Republicans on same-sex marriage as public opinion polls have shown that a majority of the party supports it. G.O.P. leaders did not officially instruct their members to vote no, according to two people familiar with the internal discussions, making the vote more a matter of personal conscience.

The bloc of Republicans who supported the measure amounted to less than a quarter of the party conference, but that was a far greater proportion than gay rights legislation has drawn in the past from G.O.P. lawmakers. Only three Republicans voted last year for sweeping legislation that would prohibit discrimination based on sex, sexual orientation and gender identity. And in 2006, just 27 House Republicans opposed an effort to amend the Constitution to bar same-sex marriage.

Tim Lindberg, an assistant professor at the University of Minnesota Morris, said there had been a shift in perception on L.G.B.T.Q. rights throughout the country, and on same-sex marriage in particular.

“There is no risk in supporting it, but there’s a political liability if you go too far right,” Mr. Lindberg said regarding same-sex marriage rights. “It’s not a measuring stick for whether you’re a conservative anymore.”

Republicans have not shown nearly as much support for other items on the Democratic agenda, such as two bills seeking to ensure access to abortion. But the vote on the same-sex marriage legislation did not show a major shift in Republican views on other social issues, said Adam Probolsky, a nonpartisan pollster and former Republican operative.

“There’s just this general realization that these so-called social aspects of the agendas are not the main reason why people are Democrats or Republicans,” Mr. Probolsky said. “Still, you hope it’s a sign of things to come. It’s good public policy being made in a way that it’s supposed to be.”

Last fall, Ms. Cheney, a staunch conservative, dropped her longstanding opposition to same-sex marriage, saying, “I was wrong.” Her sister, Mary Cheney, is gay and married with children, and Liz Cheney’s earlier opposition had caused a rift in the famous family.

“This is an issue that we have to recognize as human beings that we need to work against discrimination of all kinds in our country, in our state,” Liz Cheney told “60 Minutes” in September. “Freedom means freedom for everyone.”

Representative Nicole Malliotakis of New York, another Republican who backed the bill, said in a statement that she still feels remorse for opposing same-sex marriage more than a decade ago as a state legislator.

“In 2017, I expressed my deep regret for voting against a bill legalizing same-sex marriage in New York State while in the State Assembly six years prior,” Ms. Malliotakis said. “Every legislator has votes they regret, and to this day, that vote was one of the most difficult I’ve had to take.”

Representative Nancy Mace, Republican of South Carolina, who has previously supported same-sex marriage, said she backed the measure because it was “constitutionally sound.”

“If this gives some peace of mind to ensure the institution of marriage is protected, then that’s what I’ll vote for,” Ms. Mace said.

But most Republicans were opposed. Representative Jim Jordan of Ohio, the top Republican on the Judiciary Committee, said the measure was a bid by Democrats to delegitimize the Supreme Court.

“We are debating this bill today because it is an election year,” Mr. Jordan said. “We are here for political messaging.”

Mr. Nadler contended the legislation was a necessary response to Dobbs. Even if lawmakers accepted Justice Alito’s contention that the decision had no implications for other rights, he said, the legislation was a way for Congress to “provide additional reassurance that marriage equality is a matter of settled law.”