"I think it would be better for the Republican Party if he left the Republican Party," Kristol said on C-SPAN's "Washington Journal" Tuesday.
Kristol, the founder and editor of The Weekly Standard, argued that Paul's fellow candidates and others in the GOP are wasting time and energy trying to prevent Paul from running as a third-party candidate by placating his candidacy and giving his views credibility.
He compared Paul to former Republican presidential candidate Pat Buchanan, telling C-SPAN that Republicans unsuccessfully tried to keep him from leaving the party.
Buchanan ran as an insurgent conservative against more establishment candidates in 1992 and 1996. Although he pulled a huge upset in New Hampshire by besting Bob Dole, he failed to win the nomination, eventually leaving the party and running on the Reform Party ticket in 2000.
"A lot of people, and I was one of them, said goodbye and good riddance. You’re not in the mainstream of the Republican Party, go run as a Reform Party candidate, as an independent candidate," Kristol said, referring to Buchanan.
Kristol claimed that Buchanan's departure helped the Republican Party because his views differed so far from the mainstream.
"Ron Paul’s a little different from Pat Buchanan, but he’s no better, in my view, and I actually think the Republican Party will be benefited in the long run, but even in the short run," he said.
Paul, who has remained loyal to his themes of civil liberty, fiscal conservatism and limited government throughout the primary process, has denied interest in a third-party candidacy and has said he will remain in the Republican Party.
“I’m asked this all the time, and every time my answer is the same: I have no plans on running as a third party,” Paul said last week during a debate in Manchester, N.H.
Many Republicans worry that if Paul were to launch a third-party candidacy, he would siphon votes away from the eventual GOP nominee and help reelect President Obama.
Kristol dismissed those concerns.
"I don’t think anyone should plead with him not to run or to stay in the party. I would be comfortable in a general election if Mitt Romney or Rick Santorum or Newt Gingrich were standing as the Republican in the Reagan tradition and debating both Barack Obama and Ron Paul," he said.