The U.S. Senate on Wednesday advanced a bill that seeks to protect same-sex marriage after the Supreme Court's ruling overturning federal abortion rights.

Twelve Republican Senators joined all 50 Democrats in voting for cloture on the Respect for Marriage Act.

The legislation would codify the Supreme Court's 2015 ruling in Obergefell that struck down laws and constitutional amendments that defined marriage as a heterosexual union, ushering in nationwide marriage equality. The Respect for Marriage Act would strengthen protections on a federal level and require states to recognize all legal out-of-state marriages.

A full vote in the Senate could take place as early as Thursday.

In a statement, President Joe Biden pledged to “promptly sign [the bill] into law.”

“The Respect for Marriage Act will ensure that LGBTQI+ couples and interracial couples are respected and protected equally under federal law, and provide more certainty to these families since the Supreme Court's decision in Dobbs,” Biden said.

LGBTQ rights advocates cheered Wednesday's vote.

“Today’s strong bipartisan vote of 62-37 for cloture is an incredible victory that cannot be taken lightly – this vote was the bill’s biggest procedural roadblock, and now we steer our focus forward to the Senate’s final vote on this historic legislation,” Kelley Robinson, incoming president of the Human Rights Campaign (HRC), the nation's largest LGBTQ rights advocate, said in a statement.