Ouch. New Jersey Gov. Chris Christie turned down an offer by Sen. Rand Paul to join him for a beer and bury the hatchet in their ongoing -- and very public -- feud.

"I'm running for re-election in New Jersey. I don't really have time for that at the moment," Christie said in an interview on a local radio station.

The New Jersey governor said if he finds himself in Washington, "I'll certainly look him up." But he added: "I don't suspect I'll be there anytime soon. I've got work to do here."

Christie gave Paul the brush-off after the Kentucky senator, in an interview with Fox News, offered Wednesday to make nice with the Garden State guv.

"I think with Governor Christie it's gotten a little too personal, so we're ready to kiss and make up," Paul told Fox News. He said "anytime he would like to come down and sit at a pub right around the corner from the Senate -- we'll have a beer."

Christie's response signals a resumption of the rather personal war of words between the two prominent Republicans. Both are considered potential candidates in the 2016 presidential race, and each represents a distinct wing of the Republican Party -- which has only heightened interest in their public spat.

Christie said Thursday that he doesn't understand why Paul is so "out of whack" over this, adding "he's just trying to get attention."

The feud began when they differed over warrantless surveillance programs last week. Paul is against them, while Christie says they are needed for national security.

Paul upped the rhetoric on Sunday, when he said Christie and Rep. Peter King, R-N.Y., "are the people who are bankrupting the government and not letting enough money be left over for national defense," over their push to bring Superstorm Sandy aid to their respective states.

Christie fired back on Tuesday, accusing Paul of bringing home "pork barrel spending" to Kentucky.

"I find it interesting that Sen. Paul is accusing us of having a 'gimme, gimme, gimme' attitude toward federal spending when in fact New Jersey is a donor state and we get 61 cents back on every dollar we send to Washington. Interestingly, Kentucky gets $1.51 on every dollar they send to Washington," he said at a news conference to announce homeowner grants for northern New Jersey residents affected by Sandy.

Paul defended himself against the allegations Wednesday, calling himself one of the "most fiscally conservative members of Congress" and denying he was bringing government funds to his home state.

However, he said he does not dislike Christie, and that he wants to air out their differences over a drink.

Paul says he plans to offer Christie a written invitation to join him for a drink.

Paul's invitation is reminiscent of President Obama's 2009 so-called "beer summit" at the White House with Harvard professor Henry Louis Gates Jr. and police Sgt. James Crowley to quell a national uproar over a racially-charged dispute between the two.

The Associated Press contributed to this report.