The Senate on Saturday blocked an amendment that would ban transgender athletes from playing in women’s sports, rejecting one of President Trump’s priorities as he pressures Congress to act on a broad voting bill.

Senators were holding a rare weekend session to debate the voting legislation, which would put in place strict new requirements for voter registration and require photo IDs at the polls in an effort to prevent people in the country illegally from casting ballots.

The House passed the bill earlier this year, but the Republican president has since said he wants additional priorities added to the legislation, including the sports ban for transgender athletes and a ban on all mail-in voting.

Democrats are expected to eventually block the broader legislation. Republican senators have said repeatedly that they do not have enough support to jettison the legislative filibuster, which triggers a 60-vote threshold in the 100-member Senate, or find another workaround to pass the bill. Republicans hold 53 seats.

Still, Republicans put the legislation on the Senate floor this week for a lengthy debate as Mr. Trump has said he will not sign other bills until they pass the voting measure. Senate Majority Leader John Thune said Saturday morning that Republicans “haven’t made any final decisions about how to conclude this.”

“What we are trying to do is ensure that we are having a fulsome debate,” Thune said, and put everyone on the record “one way or the other.”

The amendment that was blocked by a 49-41 vote would penalize educational institutions that receive federal funding if they permitted individuals assigned male at birth to participate “in an athletic program or activity that is designated for women or girls.”

Mr. Trump also wants Congress to block sex reassignment surgeries on some minors as part of the debate on the voting bill. It is unclear whether the Senate will hold a vote on that.

In addition, Mr. Trump has said he wants the House-passed bill to include a ban on most mail-in balloting. The president has criticized mail-in ballots for years and used it as a centerpiece of his efforts to overturn his defeat to Democrat Joe Biden in the 2020 presidential election. A ban on mail ballots would face strong pushback from lawmakers.