Lindsey Graham won't vote for Trump or Clinton in 2016

"I'm glad we're having the convention in Cleveland, not Area 51," Graham said, citing the Nevada military base popular among UFO enthusiasts.

As for the party's July convention, South Carolina's senior senator also says he will join a growing list of veteran Republicans, including both Presidents Bush, Mitt Romney, John McCain and others, now declining to attend.

RELATED: Romney, Bushes skipping GOP convention, not backing Trump

Trump responded later Friday afternoon by issuing a statement excoriating Graham for his unsuccessful presidential campaign and representation of South Carolina.

"I fully understand why Lindsey Graham cannot support me. If I got beaten as badly as I beat him, and all the other candidates he endorsed, I would not be able to give my support either," Trump said. "Every time I see Lindsey Graham spew hate during interviews I ask why the media never questions how I single handily destroyed his hapless run for President. As a candidate who did not receive 1% in his own state -- compared to my victory at nearly 40% with many others in the race -- he has zero credibility. He was a poor representative and an embarrassment to the great people of South Carolina. Judging by the incompetent way he ran his campaign, it is easy to see why his military strategies have failed so badly -- we can't even beat ISIS!"

Trump continued to hit Graham while speaking at a rally in Omaha, Nebraska, on Friday.

"He fails with his campaign horribly, then he endorses somebody else, then he endorses (Jeb) Bush, he endorses everybody," Trump said. "He's like bad luck, as soon as he endorses the people, they drop out."

During his failed 2016 campaign, Graham was early to attack Trump in the starkest of terms -- telling voters they should tell Trump he should "go to hell."

"He's a race-baiting, xenophobic, religious bigot," Graham told CNN late last year.

Trump responded in kind, even releasing Graham's personal cell phone number in public.

On Friday, Graham joined the attack on Trump for tweeting a photo of himself eating a taco bowl and saying "I love Hispanics" on Cinco de Mayo.

"Eating a taco is probably not going to fix the problems we have with Hispanics," Graham said. "I think embracing Donald Trump is embracing demographic death."

Graham said he was a "little bit" surprised when told that former Vice President Dick Cheney was supporting Trump.

"Dick Cheney's a great man. We see the world a lot alike when it comes to foreign policy. I can understand when people want to support the nominee of the Republican Party. I would like to be able to do that, but I just can't," Graham said. "Maybe I'm the outlier here. Probably am."

Graham's refusal to support Trump is another stark illustration of the schism within the GOP -- especially in the field of candidates who ran for president.

Former Texas Gov. Rick Perry was Trump's first opponent to criticize his conservative credentials. But now, Perry tells CNN, he supports Trump.

"He is not a perfect man. But what I do believe is that he loves this country and he will surround himself with capable, experienced people and he will listen to them," Perry told CNN about Trump Thursday.

Though he is a conservative Republican, Graham worked with Clinton on several issues in the Senate. Still he says he can't vote for Clinton for president, arguing that she represents a third term of Obama.

Graham endorsed Jeb Bush after ending his own White House bid, and then even backed Cruz, a colleague he had openly said he disliked.

Wishing House Speaker Paul Ryan luck in trying to find a common conservative agenda with Trump, Graham said he will turn his attention to electing Republicans to Congress.

"If there was ever a time for the country to have conservative leadership in the House and Senate, it will be in 2017 because no matter who wins the presidency -- Clinton or Trump -- we will need some rational people up there putting brakes on some of these very bad ideas."