"We know that Kevin McCarthy has a problem in our conference. He doesn't have the full support to be Speaker," Greene announced on Rep. Matt Gaetz's Firebrand podcast.
"He doesn't have the votes that are there, because there's many of us that are very unhappy about the failure to hold Republicans accountable, while conservatives like me, Paul Gosar, and many others just constantly take the abuse by the Democrats," she stated on the episode that aired Thursday morning.
Both Greene and Gosar have been stripped of their committee duties for scaring Democrats.
Gosar was censured this month for posting a manipulated anime cartoon showing him murdering Democratic Rep. Alexandria Ocasio-Cortez.
Greene was removed from her duties after posting messages that involved anti-Semitic and Islamophobic remarks and sharing QAnon conspiracy theories.
McCarthy has been under pressure to take action against members who have used violent rhetoric, amid a rising number of threats upon lawmakers in the wake of the January 6 insurrection at the Capitol.
Though he shrugged off the issue at a press conference, explaining they could expect to get back their committee position if Republicans recaptured the House in the 2022 midterms.
Although, when Gaetz asked Greene if she recognized the sitting Republican leadership she was quick to assert her opposition.
"I can't respect leadership that doesn't hold people accountable, yet allows people like me, Paul Gosar, to be constantly trampled on and abused, and then will throw us under the bus at the first given chance. I'm really sick of it," she stated.
Greene's spokesperson Nick Dyer announced in a statement to Newsweek: "Democrats have consistently targeted Congresswoman Greene since she was sworn in on January 3. Rep. Jimmy Gomez and over 70 other Democrats have a bill to expel her. Not to mention, the Democrats destroying Congressional norms and voting to remove (Greene) from committees."
Gomez presented a resolution to expel Greene from her seat, citing her past social media posts calling for violence against Democrats and advancing extremist conspiracy theories. Seventy-three House Democrats have since signed onto the effort.
"Congresswoman Marjorie Taylor Greene has previously supported social media posts calling for political violence against the Speaker of the House, members of Congress, and former President Barack Obama," Gomez announced in a statement at the opening of this year.
"Her very presence in office represents a direct threat against the elected officials and staff who serve our government," Gomez went on.
"And it is with their safety in mind as well as the security of institutions and public servants across our country, that I call on my House colleagues to support my resolution to immediately remove Congressman Marjorie Taylor Greene from this legislative body."