Occasional adversaries Bill O'Reilly and David Letterman found something to agree on during O'Reilly's Late Show appearance Thursday -- and even agreed to high-five.

Even if they couldn't agree on why they should high-five.

After Letterman argued that the U.S. invasion of Iraq turned it into a hotbed of terrorism, O'Reilly expressed regret that it took place.

I think that that was something that should not have happened in hindsight... but I will say that I supported it because all the reportage was that Saddam Hussein did have these weapons, O'Reilly said.

Letterman decided the moment called for a high-five, standing up and holding out his hand as he cried, Come on, Billy!

O'Reilly refused, explaining, I'm not high-fiving you on a war.

Letterman kept trying to coax him out of his seat, saying it was just because, we're feelin' good and happy to see each other.

We're having a good conversation, siddown, O'Reilly said.

The remark drew laughter and some loud ohs from the audience. After an awkward moment of silence -- in which Letterman remained standing -- O'Reilly relented.

It was a much friendlier exchange than some of the past ones between the oft-cranky talk show hosts. In 2009, Letterman told O'Reilly, I think of you as a goon. In 2006, he told him, About 60 percent of what you say is crap.