President Zelensky’s visit to Washington this week comes at a critical juncture for his alliance with America as Republican leaders in Congress diverge on how to allocate more funds for Ukraine. President Biden is seeking an additional $24 billion in security and humanitarian aid for Kyiv, in line with his promise to help Ukraine for “as long as it takes” to oust Russia from its borders.

Yet ratification of Mr. Biden’s request looks increasingly uncertain thanks to a growing partisan divide in Congress about how to proceed.

The Republican House speaker, Kevin McCarthy, has told reporters that he wants more Ukraine aid to be debated on its own merits as a standalone bill, rather than attaching it to other priorities like government funding.

The Senate has different ideas. Leaders in the chamber would like to combine the Ukraine aid with other priorities, such as a short-term spending bill that will likely be needed to avoid a shutdown at the end of September.

The differing approaches threaten to become a stalemate that could easily delay future rounds of American assistance to Ukraine, raising the stakes for Mr. Zelensky as he makes his first visit to America since his surprise address to Congress at the end of 2022. In that speech, he thanked “every American” for support as Speaker Pelosi and Vice President Harris unfurled a Ukrainian flag behind him.

Nine months later, with Republicans now in control of the House, there is growing wariness among voters about continued support for Ukraine as Russia turns its invasion into a costly war of attrition. In Congress, that skepticism is concentrated among House Republicans, where many share President Trump’s “America First” approach and want to halt the aid entirely.

Washington so far has approved four rounds of aid to Ukraine in response to Russia’s invasion, totaling about $113 billion, with some of that money going toward replenishing American military equipment sent to the frontlines. Most members of the House and Senate support the aid, viewing defense of Ukraine and its democracy as a global imperative.

Mr. McCarthy has stressed the need for oversight of Ukrainian assistance — as has, notably, Senator Paul — but has also been sharply critical of Russia, assailing the country’s “killing of children” in a speech this summer. But he is juggling a desire to help Ukraine with the political realities at home, which include a demand from many in his party to slash government spending.

In some ways, attaching Ukraine aid to other pressing matters could improve the odds of passing it quickly. Some lawmakers will be more inclined to vote for Ukraine assistance if it gets included with, say, disaster relief for their home states.

Yet the maneuver would also deeply divide House Republicans and is sure to inflame critics of Mr. McCarthy who are threatening to oust him from the speakership.

“I don’t know why they would want to put that onto a CR,” Mr. McCarthy said, using Washington parlance for a short-term continuing resolution that keeps agencies funded. “I think it should be discussed on its own.”

Meanwhile, the Senate Republican leader, Mitch McConnell, has put Ukraine aid at the top of his to-do list, and has been speaking from the Senate floor for weeks about the urgency he sees to act.

He brought in inspectors general last week to brief GOP senators on how American aid is being tracked to address concerns about waste and fraud. And in one of his speeches on the Senate floor, Mr. McConnell responded to critics who say that America has borne too much of the burden on Ukraine by pointing to the assistance also flowing from European nations.

“In fact, when it comes to security assistance to Ukraine as a share of GDP, 14 of our European allies are actually giving more,” Mr. McConnell said.

House Republicans hope to bring up for a vote this week a stopgap spending bill that doesn’t include Mr. Biden’s aid package for Ukraine.

Congressman Mike Garcia of California said he’s not necessarily opposed to more Ukrainian assistance, but he said the average American doesn’t know how the war is going, and the average member of Congress can’t say, either.

“Tell us what you’re doing with the money, and let’s have a debate on the floor about this funding and not ramming it down our throats,” Mr. Garcia said.

But the Senate majority leader, Chuck Schumer, said, “I cannot think of a worse welcome for President Zelensky who visits us this week than this House proposal, which ignores Ukraine entirely.”

Congressman Michael McCaul, the top Republican on the House Committee on Foreign Affairs, voiced confidence that Ukraine aid will continue.

“It has to pass. What I hear from our NATO allies … is that if the United States is not in, the whole thing falls apart,” Mr. McCaul said.