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Sen. Marco Rubio is calling for Senate Republicans to delay their leadership elections, as more members of the party's conference in the Senate appear to be bucking Minority Leader Mitch McConnell.

"The Senate GOP leadership vote next week should be postponed," Rubio, R-Fla., tweeted Friday. "First we need to make sure that those who want to lead us are genuinely committed to fighting for the priorities & values of the working Americans (of every background) who gave us big wins in states like #Florida."

Marco Rubio speaks at Republican Party of Florida 2022 Victory Dinner

Sen. Marco Rubio, R-Fla., called for a delay in the Senate GOP's leadership elections on Friday. (Eva Marie Uzcategui/Bloomberg via Getty Images)

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Rubio is just the latest Republican to take an apparent swipe at McConnell, R-Ky. Multiple GOP Senate candidates, including Sen.-elect Eric Schmitt, R-Mo., have said they would not support McConnell for party leader for the next Congress. 

Schmitt's fellow Missourian, GOP Sen. Josh Hawley, has also attacked McConnell in recent weeks. He supported Rubio's call for a delay in leadership elections in a tweet. 

"Exactly right. I don’t know why Senate GOP would hold a leadership vote for the next Congress before this election is finished," Hawley said. "We have a runoff in #GASenate - are they saying that doesn’t matter? Don’t disenfranchise @HerschelWalker."

Sen. Cynthia Lummis, R-Wyo., also backed up Rubio, tweeting, "Second," in response to his post. 

"It makes no sense for Senate to have leadership elections before GA runoff. We don’t yet know whether we’ll have a majority & Herschel Walker deserves a say in our leadership," Sen. Ted Cruz, R-Texas, added later Friday. :Critically, we need to hear a specific plan for the next 2 yrs from any candidate for leadership."

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It is not clear there are even close to enough votes to block McConnell from being the Republicans' party leader in the next Congress. He has enjoyed significant support from GOP senators in the past, and would become the longest-serving Senate party leader ever if re-elected as the top Republican in the chamber. 

Furthermore, elections for Senate leader — unlike House speaker — are done by a simple majority of the conference, rather than a majority of the chamber. That gives McConnell significant cushion, even if several senators vocally come out against him. 

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McConnell's office did not immediately respond to a request for comment.

Fox News' Chris Pandolfo and Haris Alic contributed to this report.