Representative Marjorie Taylor Greene, Republican of Georgia, on Friday took the first step toward ousting House Speaker Mike Johnson, filing a resolution calling for his removal after he pushed through a $1.2 trillion bipartisan spending bill that enraged the hard right.

“Today I filed a motion to vacate after Speaker Johnson has betrayed our conference and broken our rules,” Ms. Greene said shortly after passage of the package, which was needed to avert a partial government shutdown after midnight.

While Ms. Greene said she would not seek an immediate vote to oust Mr. Johnson, her move was an extraordinary challenge to his leadership and the second time in less than six months that divided House Republicans have weighed firing their own speaker.

“It’s more of a warning than a pink slip,” Ms. Greene told reporters on the steps of the Capitol. “We need a new speaker.”

Ms. Greene’s resolution, filed while voting was still underway on the spending bill, set up a major test for Mr. Johnson and was yet another tumultuous moment in the rancorous year the House has experienced under a fractured Republican majority.

Ms. Greene declined to say on Friday whether she would seek to invoke a privilege available to any member of the House to force a snap vote on removing Mr. Johnson, leaving lawmakers with a number of questions and uncertainty as they depart for a planned two-week recess. But her resolution at least held out the possibility that Mr. Johnson could become the second Republican speaker to face an ouster by his colleagues, less than six months after G.O.P. rebels jettisoned Kevin McCarthy, making him the first ever to be booted from the post.

Before voting began on Friday, Ms. Greene rose on the House floor to attack the spending bill, calling it a win for Democrats and assailing measures that she said funded progressive policies.

“This is not a Republican bill; this is a Chuck Schumer, Democrat-controlled bill,” Ms. Greene said on the House floor on Friday morning.

And after its passage, she expressed outrage that Mr. Johnson had violated an unwritten but sacrosanct rule among Republicans against bringing up any legislation that does not have support from the majority of their members. Less than half of Republicans backed the bill, after a parade of them spoke out against it, complaining that it did not cut spending deeply enough or contain the conservative policy requirements they pushed for, including severe immigration restrictions.

Ms. Greene’s move was the culmination of months of dissatisfaction among right-wing lawmakers with the leadership of Mr. Johnson, an ultraconservative Republican who won unanimous backing to become the speaker in October but has infuriated his right flank by cutting a number of deals with Democrats to keep the government funded.

On Friday morning before the vote, Ms. Greene told Stephen K. Bannon, a former adviser to the Trump administration, during his “War Room” program that she was weighing whether or not to call for Mr. Johnson’s ouster on a “minute-by-minute basis.”

“Our majority has been completely handed over to Democrats,” Ms. Greene said on the floor shortly before filing her motion, echoing complaints by fellow far-right members of her party that the spending packages Mr. Johnson had agreed to constituted a failure of their majority.

“This was our power. This was our leverage. This was our chance to secure the border and he didn’t do it,” Ms. Greene told reporters before leaving the Capitol on Friday. “It is a betrayal.”

If brought to a vote, Ms. Greene’s resolution would prompt the second instance in more than 100 years that a lawmaker has used a tool that has more often been deployed as a threat by disgruntled lawmakers against their speaker than a genuine effort to oust them.

Should she move to force the issue, Ms. Greene could face a steep challenge in mustering a majority to remove Mr. Johnson. House Republicans are wary of throwing the chamber into another period of chaos, like the one that paralyzed the House for weeks after Mr. McCarthy’s ouster.

Representative Matt Gaetz, the Republican of Florida who led the charge for Mr. McCarthy’s removal, told reporters on Thursday that he would not seek the same fate for Mr. Johnson because it would run the risk of allowing a Democrat to be elected speaker.

And while Democrats unanimously backed the move to oust Mr. McCarthy last fall, they have recently signaled they would be inclined to rescue Mr. Johnson if he faced a similar threat. Representative Hakeem Jeffries of New York, the minority leader, told The New York Times that he believes “a reasonable number” of his fellow Democrats would protect the Republican speaker from removal if he faced a G.O.P. revolt for allowing a vote on a foreign aid bill that includes money for Ukraine.

Asked on Friday about the prospect of Democrats joining a coalition to rescue the Republican speaker, Mr. Jeffries said his previous comments had been “an observation, not a declaration,” adding that he would need to talk to his members “about the best way to proceed.”

Carl Hulse and Luke Broadwater contributed reporting.