Sen. Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (R-Ky.) on Thursday shot back at Sen. John McCain John Sidney McCainThe electoral reality that the media ignores Kelly's lead widens to 10 points in Arizona Senate race: poll COVID response shows a way forward on private gun sale checks MORE after the Arizona Republican accused Paul of working for Russian President Vladimir Putin.

"I think he makes a really, really strong case for term limits," Paul said on MSNBC's "Morning Joe." "I think maybe he's past his prime; I think maybe he's gotten a little bit unhinged."

McCain made the claims Wednesday from the Senate floor.

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"He has no justification for his objection to having a small nation be part of NATO that is under assault from the Russians," McCain said.

"The senator from Kentucky is now working for Vladimir Putin."

The comments came after McCain asked for unanimous consent to set up a vote on a treaty on Montenegro joining NATO, but Paul objected.

Under Senate rules, any one senator can object to a unanimous consent request. McCain warned before asking for consent that any senator who objected was "carrying out the desires and ambitions of Putin."

Paul said the U.S. military is already stretched thin.

On Thursday, the Kentucky Republican said there can be a "rational discussion" about the pros and cons of expanding NATO.

"We currently have ... combat troops in about six nations. We have troops actively just stationed in probably a couple dozen others," he said.

"We have a $20 trillion debt."

Paul said McCain's foreign policy would "greatly endanger" the country and "greatly overextend us."

"And there has to be the thought whether or not it's in our national interest to pledge to get involved with a war if Montenegro has an altercation with anyone," he said.

"Another argument is that, when you ask the people of Montenegro, only about 40 percent or slightly less are actually in favor of this," he said, adding there are a lot of considerations.

"But to call someone somehow an enemy of the state or a traitor might be considered by most reasonable people to be a little over the top."