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Kentucky Democratic Gov. Andy Beshear this week would not say whether he would appoint a Republican to succeed Sen. Mitch McConnell, R-Ky., should the GOP leader step down for health reasons.

Beshear was asked Thursday about a hypothetical Senate vacancy in the event that McConnell, 81, does not complete his current term — but the governor refused to speculate on the matter.

"There is no Senate vacancy," he told reporters. "Senator McConnell has said he's going to serve out his term, and I believe him, so I'm not going to speculate about something that hasn't happened and isn't going to happen."

McConnell's health is in the spotlight again after he froze for more than 30 seconds while fielding questions from reporters in Covington, Kentucky, on Wednesday. It was the second time the GOP Senate minority leader — the longest-serving party leader in U.S. history — froze in front of cameras this year since he fell and was hospitalized with a concussion in March.

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Andy Beshear and Mitch McConnell

Kentucky Gov. Andy Beshear greets Senate Minority Leader Mitch McConnell (R-Kentucky) and his wife, former U.S. secretary of labor and transportation Elaine Chao, at the annual St. Jerome Fancy Farm Picnic in Fancy Farm, Kentucky, on Saturday, August 5, 2023. (Ryan C. Hermens/Lexington Herald-Leader/Tribune News Service via Getty Images)

The episodes have raised questions about McConnell's ability to continue serving as GOP leader and fueled speculation about whether he will resign from the Senate. After the first episode in July, McConnell said he intends to complete his current term, which ends in 2026 when he would be 84. 

Beshear pointed to McConnell's previous statements when pressed on the issue Thursday.

"Well, I respect Sen. McConnell and his health enough, first of all, not to sensationalize it and, second, there is no vacancy. So he has said he's going to serve out his term, and I fully believe him," Beshear said.

In 2021, the GOP-dominated state legislature overrode Beshear's veto and enacted a law that limited the governor's ability to fill congressional vacancies. Were McConnell to resign, Beshear would be obligated by state law to appoint an interim senator from a list of nominees submitted by the state executive committee of the outgoing senator's party, in this case, the Republican Party. 

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Kentucky Gov. Andy Beshear speaks at a podium

Andy Beshear, governor of Kentucky, speaks during an event in Covington, Kentucky, on Wednesday, January 4, 2023. (Joshua A. Bickel/Bloomberg via Getty Images)

Previously, the governor could appoint a replacement to fill a vacant Senate seat until the next general midterm elections, which happen every two years. 

In his veto statement, Beshear said the bill "improperly and unconstitutionally" restricts his power to fill Senate vacancies. 

The law "upends a century of precedent by delegating the power to select the representative of all Kentuckians to an unelected, unaccountable committee of an organization that represents only a fraction of Kentuckians," Beshear said in 2021. 

McConnell was cleared to return to work by his doctor on Thursday. 

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"I have consulted with Leader McConnell and conferred with his neurology team. After evaluating yesterday’s incident, I have informed Leader McConnell that he is medically clear to continue with his schedule as planned," Dr. Brian Monahan, Congress' attending physician, wrote in a note Thursday.

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"Occasional lightheadedness is not uncommon in concussion recovery and can also be expected as a result of dehydration," Monahan added.

Fox News' Kyle Morris contributed to this report.