A group of right-wing House Republicans pushing to load up the annual defense bill with socially conservative policies on abortion, race and gender have another demand: severe restrictions on U.S. military support for Ukraine.

The pressure raises the prospect of a divisive floor fight over America’s backing for the war effort just as President Biden tries to rally European allies to support Kyiv in its conflict with Russia.

The group’s proposals on military aid stand no chance of passing the House, where there continues to be strong bipartisan support for backing Ukraine’s war effort, or going anywhere in the Senate. But the far right’s insistence on casting votes on the matter anyway has further imperiled the defense legislation and transformed what is ordinarily a broadly supported measure that provides the annual pay raise to U.S. military personnel and sets Pentagon policy into a partisan battleground that has placed Republican divisions on display.

The House on Wednesday began debating the $886 billion measure, sidestepping the rifts as Republican leaders toiled behind the scenes to placate ultraconservative lawmakers who are demanding votes to scale back Ukraine aid and add social policy dictates. But those disputes will eventually have to be resolved to pass the bill, which had been expected to receive approval on Friday — a timetable that is now in doubt as the hard right threatens to hold up the process.

They are seeking votes on a series of proposals that would hamstring U.S. support for Ukraine, including one to curtail all funding for Kyiv until there is a diplomatic solution to the conflict and another that would end a $300 million program to train and equip Ukrainian soldiers that has been in place for nearly a decade.

“Congress should not authorize another penny for Ukraine and push the Biden administration to pursue peace,” Representative Marjorie Taylor Greene, Republican of Georgia, argued to lawmakers on the House Rules Committee this week, appealing to them to allow votes on several proposals she has written on the topic. “Ukraine is not the 51st state of the United States of America.”

Representative Scott Perry, Republican of Pennsylvania and the chairman of the conservative House Freedom Caucus, said votes to curtail support for Ukraine were every bit as important to the members of his group as votes to restrict abortion access and services for transgender soldiers. Asked whether some might seek to block the bill without such votes, he replied: “They might.”

Because Speaker Kevin McCarthy holds only a slim margin of control in the House, any rebellion by the right wing could stop the defense measure in its tracks, denying him the votes he would need from his side to advance it to final passage. But if he bows to the demands for votes on Ukraine, it would put divisions in Congress over the war on display at a critical junction in Ukraine’s counteroffensive, and just after Mr. Biden has appealed to allies this week during a NATO summit to remain united in support.

“We can see from what’s taken place at the NATO summit, the significance and importance of us all speaking with one voice and making sure that we’re giving the Ukrainians what they need to win this war,” Representative Gregory W. Meeks of New York, the top Democrat on the Foreign Affairs Committee, said in an interview on Wednesday. “It will be absolutely the worst thing to do to have a show of division — that’s playing right into Putin’s hands.”

Some mainstream Republicans say they relish the fight, seeing it as a potential opportunity to put the rebellious right wing of the party in its place.

“It’s going to fail big time,” Representative Mike D. Rogers, Republican of Alabama, said of the hard right’s bid to scrap American support for Ukraine. “So I hope they make it in order — I think you’ll see it go down overwhelmingly.”

The defense bill is the latest forum right-wing lawmakers have been using to challenge Mr. McCarthy’s leadership. Their protest, which began during January’s protracted speaker fight, resumed last month, when 11 far-right lawmakers brought the House floor to a standstill to express their fury at Mr. McCarthy’s debt ceiling deal with President Biden. They have threatened similar tactics in the future if he fails to bow to their demands.

Mr. McCarthy had been bracing for a difficult fight over Ukraine funding in the coming months, when the Biden administration is expected to request billions of dollars to keep Kyiv’s war machine humming.

Hoping to head off a revolt from the right wing, the speaker publicly declared he was opposed to any additional funding for Ukraine beyond the limits of the debt ceiling deal, despite having publicly proclaimed just weeks before: “I vote for aid for Ukraine, I support aid for Ukraine.”

But with the defense bill, the ultraconservative faction is trying to force the issue now.

Ms. Greene, who has become one of Mr. McCarthy’s closest allies, demurred on Wednesday when asked whether she would help other right-wing members block progress on the bill if leaders denied her a vote to curtail Ukraine funding. Ms. Greene, despite being one of the most outspoken hard-right members of the House, has routinely taken Mr. McCarthy’s side in disputes with his rank and file, and has refused to lend any support to the efforts to undermine his leadership. But her involvement is an indicator of how deeply a vote on Ukraine might split House Republicans.

Ukraine assistance is a tricky issue for the G.O.P. politically. Both of the front-runners for the 2024 Republican presidential nomination, former President Donald J. Trump and Gov. Ron DeSantis of Florida, have said they would like to limit U.S. assistance to Ukraine. According to a recent poll by the Ronald Reagan Presidential Foundation and Institute, while more than 70 percent of Republicans want to see Ukraine win the war, only half support sending U.S. military aid to help the country defeat Russia.

Last year, 57 House Republicans voted against a measure to provide $40 billion in military and humanitarian assistance for Ukraine. Congress approved a total of more than $113 billion in Ukraine aid last year.

House G.O.P. leaders expressed confidence on Wednesday that they could defeat any proposal to strip funding for Ukraine, thus preserving the integrity of the underlying defense bill. But they worried aloud about the social policy measures, which they noted would alienate Democrats whose votes would be needed to pass the bill.

Ultraconservatives are pushing for votes on proposals that would undo a Pentagon policy offering time off and travel reimbursement to service members traveling out of state to obtain an abortion, to end diversity training in the military, and to ensure that medical services for transgender troops are limited.

“Those I think are actually dicier,” said Representative Tom Cole, Republican of Oklahoma and the chairman of the Rules Committee. “You’re not going to get any Democrats that way.”

G.O.P. leaders appealed to their colleagues on Wednesday to support the bill as is, highlighting provisions already included that would ban drag shows at military installations and the teaching of critical race theory.

“This bill goes after the woke, failed, far-left policies that far-left Democrats have wrongfully forced onto the Department of Defense and our men and women in uniform,” Representative Elise Stefanik of New York, the No. 4 Republican, told reporters.