“I think with Gov. Christie, it’s gotten a little too personal, so let’s kiss and make-up," Paul said on Fox News' "Your World with Neil Cavuto." "We're going to have to patch things up. If we can sit down -- I'm inviting him for a beer anytime he would like to come down and sit down at the pub right around the corner from the Senate."

Paul said he would soon formalize the offer.

He added: "I think it's time to dial it down. I think we've got enough Democrats to attack. I've said my piece on this. I don't like Republicans attacking Republicans because it doesn't help the party grow bigger."

In recent days, Christie has targeted Paul and other libertarians for voting to defund the NSA's phone record collection program. Paul hit back Monday by suggesting Christie was exploiting 9/11 victims. By the end of the day Tuesday, Christie noted that Kentucky gets much more federal assistance per capita than New Jersey, and Paul labeled Christie the "king of bacon."

Even as he was proposing a cease-fire, though, Paul said it was a "stupid argument" to blame him for Kentucky's federal aid -- much of which is based on poverty formulas and the fact that Kentucky has military bases.

Update 8:39 a.m. Thursday: Christie has declined Paul's offer.

“I’m running for re-election in New Jersey,” Christie said during his regular radio show on New Jersey 101.5. “I don’t really have time for that at the moment. … I’ve got work to do here.”

Christie did say he'd look Paul up if he found himself in Washington, but he also accused Paul of being "childish."

“I didn’t use any childish phrases like, ‘gimme, gimme, gimme,’" Christie said. "He did, and I just have to assume from that that he’s trying to get some attention. And that’s fine. He’s not the first politician to use me to get attention in the national media and I’m sure he won’t be the last."