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.