Kentucky Sen. Rand Paul escalated an already-tense war of words with Arizona Sen. John McCain Thursday morning, by suggesting that it's time for McCain to leave the Senate.

McCain on Wednesday accused Paul of working for Russian President Vladimir Putin because he blocked a treaty that would allow Montenegro to join NATO. Paul dismissed that and fired back at McCain on MSNBC.

"You know, I think he makes a really, really strong case … for term limits," Paul said. "I think maybe he's past his prime. I think maybe he's gotten a little unhinged."

On Wednesday, McCain tried to call up the treaty on the floor of the Senate and said of anyone who blocked it, "they are now carrying out the desires and ambitions of Vladimir Putin, and I do not say that lightly."

Paul, who was expected to block it, did so and then quickly left the Senate floor. McCain said, "The senator from Kentucky is now working for Vladimir Putin."

Paul said his objection was to the idea that American soldiers would need to go fight a war in Montenegro if it became embroiled in some conflict. He said Thursday that he doesn't believe Americans want to go and die in a war that otherwise wouldn't involve American interests.

He said McCain's foreign policy would be dangerous for the country.

"His foreign policy is something that would greatly endanger the United States, greatly overextend us and there has to be some though if it's in the United States' interests to get involved," he said.

Paul said he disagreed with the notion of wanton expansion of NATO, and said there's a bipartisan consensus in Washington that NATO should be as big as possible. If that happened, the U.S. would be at war over Ukraine and Georgia right now because the Russians invaded both, he said.

"There's a real debate about how big NATO should be and whether or not it's been more provocative than good," he said. "We seem to be paying for all of it. Whenever there's a war fought, our soldiers fight it and our dollars pay for it."