President Biden appealed to Congress on Thursday for an additional $24 billion to help Ukraine defeat Russia’s invasion, setting up a major test of whether the expansive war effort retains the bipartisan support it has enjoyed since Moscow sent troops across the border nearly 18 months ago.

The request, part of a larger $40 billion spending package that would also pay for disaster relief and border enforcement, is the first time Mr. Biden has asked lawmakers to send more arms to Ukraine since Republicans took over the House in January promising not to “write a blank check” for the war.

The spending package comes as polls have detected growing weariness over the war among an American public focused on problems at home. Allied leaders in Europe and elsewhere are watching nervously to see if the United States will pull back from its leadership of the international coalition backing Ukraine, while analysts say that President Vladimir V. Putin of Russia is gambling that he can wait out the West.

Mr. Biden has made his support for Ukraine a signature of his foreign policy, arguing that it is vital to American national security to stand up to naked aggression in Europe. American weapons have been critical to Ukraine’s success in resisting Russian forces. But former President Donald J. Trump, who has praised Mr. Putin’s aggression as “genius” and refused to express support for a Ukrainian victory, could make the war a central issue in next year’s election.

“The president has reaffirmed that we will stand with Ukraine as it defends its sovereignty for as long as it takes, a strategy that has successfully united our allies and partners and equipped Ukraine to defend itself against Russian aggression,” Shalanda D. Young, the director of the White House Office of Management and Budget, wrote in a letter to Speaker Kevin McCarthy, Republican of California.

Mr. McCarthy said in June that any supplemental appropriation request for Ukraine was “not going anywhere” and that additional aid would have to be worked out in the regular congressional spending process. Seventy House Republicans voted last month to cut off aid to Ukraine altogether.

Although that indicates that a bipartisan majority remains in the full House, it was unclear if Mr. McCarthy would defy such a large and vocal segment of his conference to enable the package to get to the floor intact. Mr. McCarthy offered no immediate response to the president’s proposal on Thursday.

The request includes $13.1 billion for military aid to Ukraine and replenishment of Pentagon weapons stocks used for the war effort. An additional $8.5 billion would go for economic, humanitarian and other assistance to Ukraine and other countries affected by the war, and $2.3 billion would be used to leverage more aid from other donors through the World Bank.

Congress has already approved $113 billion in military, economic, humanitarian and other aid for Ukraine, including around $70 billion for war fighting. Of that total, around 90 percent has already been spent or is already designated to be spent. The United States is by far the largest donor to Ukraine, a point of contention for some critics, although the Council on Foreign Relations has calculated that based on share of economy, it is the 12th largest backer of Ukraine, behind Britain, Poland, Norway and others.

Some conservative critics of Ukraine aid vowed to press Republicans to draw a line. The Heritage Foundation, which has been a leading voice on the right criticizing American help for Ukraine, issued a statement on Thursday insisting that no more money be allocated unless the Biden administration does more to account for what has been spent and articulates “a plan that defines the end goal.”

Dan Caldwell, the vice president of the Center for Renewing America, a right-wing think tank influential among House Republicans and Freedom Caucus members, said Mr. McCarthy should keep his promise not to approve more aid. “Congress should not spend billions more in support of continuing a war in which there are no vital American interests at stake and where there remains a real risk of nuclear escalation,” Mr. Caldwell said.

Some Freedom Caucus members and their allies quickly responded in kind. “No,” Representative Chip Roy, Republican of Texas and the caucus’s policy director, wrote on X, the platform formerly known as Twitter. “This should be a non-starter for the @HouseGOP. It’s time to stand up for Americans and against the uniparty.”

Supporters of Ukraine said the debate over the spending package could be a critical juncture in the war, sending a message to the Kremlin about American fortitude.

“The only way Putin can win this war now is for the United States to stop helping Ukraine,” former Representative Tom Malinowski, Democrat of New Jersey, said in an interview. “McCarthy’s going to have to decide whether he wants House Republicans to be blamed for that even though most Republicans in Congress, if given a chance, would vote to keep sending help.”

Mr. Biden sought to sweeten the pot by adding politically popular spending to the Ukraine aid. The supplemental appropriation request includes $12 billion for disaster relief, $4 billion for border security and $60 million for wildland firefighter pay. Democrats cheered money to fight fentanyl trafficking and child labor violations.

But the combined request will challenge the spending limits that Mr. Biden negotiated with Mr. McCarthy in May as part of a deal to increase the debt ceiling. Just this week, the Congressional Budget Office estimated that the federal government spent $1.6 trillion more than it took in during the first 10 months of the fiscal year, more than twice the shortfall during the same period a year earlier.

The politics of Ukraine have changed drastically since the invasion in February 2022. With Mr. Trump leading the way, a number of Republican leaders have questioned American involvement in the war.

Mr. Trump has gone so far as to link future security aid to Ukraine to his efforts to tarnish Mr. Biden at home, much as he did while president in actions that got him impeached. At a rally last month, he said Congress should refuse to send any more weapons until the F.B.I., I.R.S. and Justice Department “hand over every scrap of evidence they have on the Biden crime family’s corrupt business dealings” and threatened to sponsor primary challenges to Republicans who resisted.

Other Republican presidential candidates, including former Vice President Mike Pence, Senator Tim Scott of South Carolina and Nikki R. Haley, the former ambassador to the United Nations, have stood firmly by Ukraine and in some cases criticized Mr. Trump for appeasing Mr. Putin.

Fifty-five percent of Americans now oppose more aid to Ukraine, according to a poll released by CNN last week. The party breakdown is stark — 71 percent of Republicans oppose additional assistance, while 62 percent of Democrats favor it.

The White House consulted with key Republicans in Congress before making its request and is counting on help from Senator Mitch McConnell of Kentucky, the Republican minority leader. Mr. McConnell has been a staunch supporter of Ukraine and, unlike Mr. Trump and Mr. McCarthy, has pushed Mr. Biden to do more, not less.

“I look forward to carefully reviewing the administration’s request to make sure it is necessary and appropriate to keep America safe, secure our borders, support our allies and help communities rebuild after disasters,” Mr. McConnell said in response to the spending request.

It remains unclear how much influence Mr. McConnell has over Mr. McCarthy, though. To win the speakership in January after 15 arduous rounds of voting, Mr. McCarthy agreed to install three hard-right conservatives on the House Rules Committee, which determines whether bills get on the floor. Even if Mr. McCarthy reverses himself and agrees to put a Ukraine package on the floor, he would have to enlist one of the conservatives or rely on Democratic votes, which he does not want to do.