Senate GOP Leader Mitch McConnell is medically cleared to continue his schedule, the US Capitol physician said Thursday, after he froze for the second time in as many months in public.

The statement comes as McConnell moved behind the scenes to reassure his allies and donors he can do his job -- even as questions persist over how long the 81-year-old Kentuckian will stay as Republican leader.

"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, the attending doctor for the Capitol, said in a statement released through McConnell's office.

"Occasional lightheadedness is not uncommon in concussion recovery and can also be expected as a result of dehydration," added Monahan. McConnell's office has previously said that his freezes were due to lightheadedness and dehydration.

McConnell, who has served for 16 years as the GOP leader, the longest of any Senate leader in history, has repeatedly made clear he's staying in his job until the end of next year when the 118th Congress ends -- something his confidantes say hasn't changed even after his recent health scares.

But McConnell has consistently sidestepped questions about whether he would run for leader in the next Congress, which begins in 2025. And there's some initial chatter among a handful of rank-and-file Republicans to try to force a special conference meeting to talk about their party's leadership after McConnell's latest incident, according to a person familiar with the matter.

No meeting has been called and it's unclear if one will be. It takes just five GOP senators to call for a meeting, and then at that point it would be scheduled by Sen. John Barrasso, the GOP conference chairman. Even if they have a meeting, there's no mechanism to force a vote on the party's leadership. That wouldn't happen until after the 2024 elections. But such a meeting would draw more focus on McConnell's health.

While it's uncertain if Republicans will force such a meeting, the Senate GOP conference is set to meet for its usual weekly meeting next Wednesday, giving the GOP leader the opportunity to address his conference for the first time on the matter.

Following a recent concussion after falling and hitting his head in March, coupled with his two public frozen moments, Republican senators and aides told CNN they are doubtful he will try to run for the job again -- potentially opening up the GOP leadership role for the first time since McConnell took the reins in 2007.

McConnell, who disdains the focus on his health, has so far refused to publicly disclose the reason why he froze up for roughly 30 seconds two separate times this summer -- the latest on Wednesday in Covington, Kentucky -- other than his aides saying he felt "lightheaded" and that he would consult a physician.

But McConnell's office has not disclosed the doctor's diagnosis. And the topic did not come up when the GOP leader later attended a Wednesday fundraiser for Rep. Jim Banks, who is running for a Senate seat in Indiana. Several sources said that McConnell didn't discuss his viral moment from earlier in the day.

But two attendees told CNN that he engaged with the crowd and acted normally, reassuring his donors and allies that he can do the job. Asked about McConnell, Banks said that the Republican leader was "sharp" and "engaging" and "very dialed in on my race and following closely."

"Tough as nails," another attendee said when describing McConnell's demeanor.

Following the episode on Wednesday, McConnell was on the phone with several GOP senators -- including his potential successors -- to tell them he was fine.

"The leader sounded like his usual self and was in good spirits," said Ryan Wrasse, a spokesman for Senate GOP Whip John Thune, who spoke to the GOP leader.

Kelley Moore, a spokeswoman for Sen. Shelley Moore Capito, confirmed McConnell spoke with the West Virginia Republican, a member of his leadership team.

"Sen. Capito said the leader sounded fine and she looks forward to seeing him on Tuesday when the Senate returns," Capito's spokeswoman said.

McConnell's last freeze-up occurred right before senators left for a five-week August recess. Some at the time wanted more information about McConnell's health -- questions that are bound to intensify next week when they return to session.

"Obviously his first responsibility is to the voters of Kentucky," GOP Sen. Kevin Cramer of North Dakota told CNN in July. "But once you become the leader, your responsibilities obviously are with other constituents, mainly, at least in his case, 48 of his closest friends."

Cramer said at the time that McConnell "should tell us if something bigger is going on," adding: "Clearly there's a greater responsibility for transparency."

Thune and Barrasso and Sen. John Cornyn are seen as likely successors to McConnell, but they have continued to support him even during his health scares.

Asked before the recess if he was preparing to run for leader, Cornyn said: "Those elections won't be until November 2024. So just the short answer is, there's nothing to prepare for."