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Embattled Texas Attorney General Ken Paxton, a Republican, teased a potential 2026 primary challenge to Texas Sen. John Cornyn after the lawmaker announced his bid to succeed Minority Leader Mitch McConnell come November. 

Paxton took to X, formerly Twitter, Wednesday night — prior to Cornyn revealing his intention to run for leader — addressing speculation about it. Paxton said the senator would have difficulty remaining in his role "since he is anti-Trump, anti-gun, and will be focused on his highly competitive primary campaign in 2026."

Despite Paxton's claim, Cornyn endorsed former President Trump for president last month, calling on Republicans to rally around him. 

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KEN Paxton and John Cornyn

Texas Attorney General Ken Paxton, left, teased a potential 2026 primary challenge to Texas Sen. John Cornyn. (Brett Coomer/Houston Chronicle via Getty Images | Kevin Dietsch/Getty Images)

The attorney general's accusation of Cornyn being "anti-gun" is likely a reference to his involvement in crafting and bolstering the Bipartisan Safer Communities Act, a gun reform bill taken up following the Uvalde elementary school shooting in the Lone Star state. Cornyn pioneered the bill alongside senators Kyrsten Sinema, I-Ariz., Chris Murphy, D-Conn., and Thom Tillis, R-N.C.

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Paxton didn't note in his post who would be competing against Cornyn in a primary, but he also hasn't dismissed speculation he would challenge Cornyn. Representatives for Paxton did not respond to Fox News' inquiries about a potential Senate run. 

"Republicans deserve better in their next leader and Texans deserve another conservative Senator," Paxton wrote on X.  

"Hard to run from prison, Ken," Cornyn posted to X shortly afterward, referencing Paxton's legal trouble. In April, the attorney general heads to trial on charges related to securities fraud in a case that has been delayed since an initial indictment more than eight years ago. Paxton was acquitted late last year of 16 articles of impeachment that alleged various acts of bribery and corruption following a highly publicized Texas Senate trial. 

After McConnell's surprise announcement Wednesday that he would step down as Republican Senate leader, Cornyn told reporters, "Not today," noting the day "is about Mitch McConnell." But, he added, "I've made no secret about my intentions."

On Thursday morning, the Texas Republican announced his bid for leader of the Republican conference. 

"I am asking my Republican colleagues to give me the opportunity to succeed Leader McConnell," Cornyn said in a statement. 

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"I believe the Senate is broken — that is not news to anyone," he said. "The good news is that it can be fixed, and I intend to play a major role in fixing it."

Cornyn was the first to announce his campaign for the role, though several others are expected to join the race. 

Paxton responded to the news on X, posing a poll to his followers.

"John Cornyn has waved the white flag on election integrity, border security, protecting the 2nd amendment, and everything else constitutional conservatives care about. Do you think he's conservative enough to lead Republicans in the Senate?" Paxton asked. 

The poll had received more than 13,000 votes by the afternoon, with the overwhelming majority saying "No."

A Paxton campaign spokesman told Fox News Digital Thursday that "Texas deserves another conservative senator. All options are on the table."

Cornyn's office declined to comment when reached by Fox News Digital.

Get the latest updates from the 2024 campaign trail, exclusive interviews and more at our Fox News Digital election hub.