Representative Marjorie Taylor Greene on Tuesday escalated her threat to oust Speaker Mike Johnson, distributing a scathing letter that made the case for his removal and took Republicans to task for tolerating his leadership.

In a five-page memo sent to her colleagues on Tuesday morning, a copy of which was obtained by The New York Times, Ms. Greene, a right-wing Republican from Georgia, assailed Mr. Johnson with a point-by-point takedown of his record as speaker. She accused him of fecklessly advancing President Biden’s agenda and wasting opportunities to advance G.O.P. priorities.

Ms. Greene warned her colleagues that they risked falling out of touch with their voters if they continued to accept what she called “a complete and total surrender” by Republicans under Mr. Johnson.

The letter left little doubt that Ms. Greene, who filed a resolution last month calling for Mr. Johnson’s removal but said it was merely “a warning,” intends to follow through on her threat to call a vote on unseating him.

“If these actions by the leader of our conference continue, then we are not a Republican Party — we are a uniparty that is hellbent on remaining on the path of self-inflicted destruction,” she wrote. “I will neither support nor take part in any of that, and neither will the people we represent.”

Her intensified threat came at a tricky time for Mr. Johnson, who has said he will soon bring up an emergency national security spending package that includes aid to Ukraine, something that has enraged the far right. He is also planning to hold a set of tough votes this week on legislation to renew a warrantless surveillance program that many in his party oppose.

In the letter, Ms. Greene ticked through the many instances since Mr. Johnson took the gavel five months ago when he has negotiated with Democrats on major legislation — including multiple federal spending bills to prevent the government from shutting down and the annual defense bill to ensure American troops receive a pay raise — and cut deals she called a betrayal of Republican values. His actions have “angered our Republican base so much and given them very little reason to vote for a Republican House majority,” she wrote.

And she condemned members of her party, adding, “If we win the House this fall, it will only be because President Trump is on the ballot, not because we have earned it.”

Much of her criticism stemmed from Mr. Johnson’s decision last month to push through a $1.2 trillion bipartisan government spending bill — one that passed with a majority of Republicans voting against it — that prompted Ms. Greene to file the resolution calling for Mr. Johnson’s removal.

She said at the time that the move was “more of a warning than a pink slip,” raising questions about whether she planned to demand a snap vote to oust Mr. Johnson or was simply seeking the outsize attention that came with threatening to. The House then left Washington for a two-week recess.

Mr. Johnson hoped the break would help cool tensions that threatened his hold on the job. In interviews, he referred to Ms. Greene as a friend. He said that he shared her frustrations about spending legislation and that they had been texting and planned to meet when they returned to Washington.

Now the House is back, and Ms. Greene is making it clear she will not be easily mollified.

“Fully funding abortion, the trans agenda, the climate agenda, foreign wars and Biden’s border crisis is not ‘ensuring liberty, opportunity and security for all Americans,’” she wrote, quoting from a list of Mr. Johnson’s key priorities upon taking the post.

She also slammed Mr. Johnson for failing to defund what she called a “witch hunt” by Jack Smith, the special counsel who is prosecuting Mr. Trump for trying to overturn the 2020 election and for mishandling classified documents. Taken together, she said, those would result in a “death sentence” for Mr. Trump.

“They want him dead,” Ms. Greene said of Democrats, “and our power of appropriations could have stopped it, but Speaker Johnson didn’t even try.”

(It is all but unthinkable that Democrats would have agreed to slash spending for Mr. Smith’s prosecutions, or that Mr. Biden would have signed legislation doing so.)

On Monday night, Ms. Greene also laid out her case against Mr. Johnson to voters at a town hall in Tunnel Hill, Ga. “Am I angry? Yes,” she said. “My question is, are you angry?”

Ms. Greene’s letter appeared aimed largely at making the speaker squirm over the Ukraine aid bill, which he has agonized over — first refusing to take it up but more recently bowing to entreaties by Mr. Biden, Democrats, other Republicans and world leaders to do so.

“Mike Johnson is publicly saying funding Ukraine is now his top priority when less than seven months ago he was against it,” Ms. Greene wrote. “The American people disagree — they believe our border is the only border worth fighting a war over, and I agree with them.”

For months, Ms. Greene has been calling the Ukraine measure her “red line” for ousting the speaker. Last week, in an interview with the right-wing media host Tucker Carlson, Ms. Greene wondered aloud whether Mr. Johnson was being blackmailed to bring it up, “because he’s completely disconnected with what we want.”

Ms. Greene, a rabble-rouser who forged an unlikely alliance with former Speaker Kevin McCarthy that got her kicked out of the hard-right House Freedom Caucus, referred to herself in the letter as a “team player,” but one who can no longer support the current leadership if it continues on its current trajectory.

She ridiculed the notion of the need for compromises in a moment of divided government.

“Even with our razor-thin Republican majority, we could have at least secured the border, with it being the No. 1 issue in the country and being the issue that is causing Biden to lose in poll after poll,” Ms. Greene wrote. “Nothing says shooting within our own tent like a Republican speaker of the House who makes his rank-and-file members vote to fund full-term abortion in order to pay our military soldiers.”

It is not clear whether Ms. Greene’s arguments will persuade her colleagues, including some other hard-right members who have voiced skepticism about a second move to oust a speaker. Representative Matt Gaetz, the Florida Republican who led the charge to remove Mr. McCarthy, for instance, said that when he made his move in October, “I made a promise to the country that we would not end up with a Democrat speaker.” With the Republican majority in the House having dwindled down to one precarious vote since then, Mr. Gaetz said, “I couldn’t make that promise again today.”

In her letter, Ms. Greene said that would not happen unless more Republicans retired and the party lost its majority, or Republicans voted for Representative Hakeem Jeffries, Democrat of New York and the minority leader.