Congressman Matt Gaetz, who is threatening to fight to remove Speaker McCarthy from his position, has said that the speaker must answer for what he calls a “secret Ukraine deal” he allegedly brokered behind closed doors with President Biden. Mr. Gaetz told reporters outside the Capitol on Monday that his effort to remove the speaker, known as a motion to vacate, will be filed “this week.”

Speaking on the House floor on Monday afternoon, Mr. Gaetz said the speaker had made a “secret side deal on Ukraine” aid funding with members of the Biden administration without informing his fellow House Republicans. Mr. Gaetz said that in order “to extend Joe Biden’s spending and policy priorities, the Speaker of the House gave away to Joe Biden the money for Ukraine that Joe Biden wanted.”

“It is going to be difficult for my Republican colleagues to call President Biden ‘feeble’ while he continues to take Speaker McCarthy’s lunch money in every negotiation,” Mr. Gaetz said, referring to a debt limit and spending deal made earlier this year by the speaker and the president that did not satisfy House conservatives. 

Should Mr. Gaetz follow through on filing the motion to vacate this week — as he told reporters on Monday — then it would likely kick off a series of votes similar to the 15 rounds that it took Mr. McCarthy to win the speakership in January. Mr. Gaetz has promised to continue introducing the motion to vacate even if Mr. McCarthy continues to win the gavel.

During a Sunday appearance on “Face the Nation,” Mr. McCarthy was asked about Mr. Gaetz’s threat to oust him. “I’ll survive,” he said. “This is personal with Matt. … He’s more interested in securing TV interviews than doing something.”

On Saturday, the House passed a short-term funding deal, known as a continuing resolution, to keep the government open at current funding levels through the middle of November. In order to pass the legislation, Mr. McCarthy had to rely on the Democratic caucus, which almost unanimously voted for the proposal. Only one member opposed it because it did not include additional funding for Ukraine. On the GOP side, 90 members voted against the short-term extension. 

The Senate quickly took up the legislation and passed it, with 88 members voting in the affirmative. The sticking point for the upper chamber, though, was a lack of aid for Ukraine, as that ultimately was not included in the final bill. Senators Schumer and McConnell had previously tried to go around the House by introducing their own continuing resolution that included $6 billion in funding for the besieged nation. 

Mr. Gaetz on Monday made the so-called secret deal the crux of his argument in favor of ousting Mr. McCarthy, saying it was evidence of the speaker’s duplicitousness and lack of strength. The path to the end of the speaker’s career, Mr. Gaetz said, is a “yellow brick road that has been paved by Speaker McCarthy.” 

The Florida congressman argued that Mr. McCarthy must “demand that the United States Senate take up our single-subject” appropriations bills, one by one, though the Democratic-controlled Senate has already balked at the prospect of passing a restrictive immigration bill and other spending cuts demanded by House Republicans. “It is becoming increasingly clear who the Speaker of the House works for, and it is not the Republican conference,” Mr. Gaetz said. He concluded his remarks by saying he would be waiting for the speaker to address his concerns in the coming days. 

One Republican who has long supported Mr. McCarthy, Congressman Tom McClintock, spoke just before Mr. Gaetz on the House floor, urging his fellow Republicans not to oust the speaker for fear that Democrats could work with a small number of moderate House Republicans to elect a “coalition speaker” who would be far less conservative than the incumbent. 

“A coalition speaker will move the administration of the House sharply to the left,” Mr. McClintock said on the floor. “I implore my Republican colleagues to look past their prejudices, their passions, and their selfish views” to keep Mr. McCarthy in the speaker’s chair. 

It appears a large bipartisan group in the Senate may try to force Mr. McCarthy to bring up additional funding for Ukraine before the federal budget is finalized in mid-November. Shortly after the Senate passed the continuing resolution on Saturday night — mere hours before the government was set to shut down — Messrs. Schumer and McConnell released a statement saying they would push for aid in the coming weeks. 

“We welcome today’s agreement to avoid a harmful and unnecessary shutdown of the federal government,” the Democratic and Republican leaders wrote. “Nevertheless, this agreement leaves a number of urgent priorities outstanding. In the coming weeks, we expect the Senate will work to ensure the U.S. government continues to provide critical and sustained security and economic support for Ukraine.”

The letter was also signed by the top Democrat and Republican on the Appropriations Committee, Senators Murray and Collins, as well as the leaders of the subcommittee that deals with foreign aid, Senators Coons and Graham.