Graham is the highest GOP office holder so far to rule out voting for Trump.
Other Republicans, such as Sen. Ben Sasse (R-Neb.), have also said they won't support Trump in the fall, while Speaker Paul RyanPaul Davis RyanAEI names Robert Doar as new president GOP can't excommunicate King and ignore Trump playing to white supremacy and racism House vote fails to quell storm surrounding Steve King MORE (R-Wis.) said Thursday he couldn't yet support the controversial businessman.
“It’s hard to believe that in a nation of more than 300 million Americans Hillary ClintonHillary Diane Rodham ClintonTrump knocks BuzzFeed over Cohen report, points to Russia dossier DNC says it was targeted by Russian hackers after fall midterms Special counsel issues rare statement disputing explosive Cohen report MORE and Donald Trump will be our choices for president," Graham said in a statement released by his Senate office. 

Graham said he'd "absolutely" not support Clinton, the overwhelming favorite for the Democratic nomination, saying she'd represent President Obama's "third term."

“I also cannot in good conscience support Donald Trump because I do not believe he is a reliable Republican conservative nor has he displayed the judgment and temperament to serve as commander in chief," said Graham, who ran for president against Trump during the GOP primary.

Graham said after the November election he'd work with the next president to "deal with the many challenges facing our nation." 

“I will enthusiastically support Republicans for other offices in South Carolina and throughout the country," he said, adding his focus was on supporting Republicans in the House and Senate. 
Graham also announced he doesn't plan to attend the GOP convention in July in Cleveland. Several prominent Republicans, such as Mitt Romney and Jeb Bush, have said they don't intend to go, either.
Graham admitted his position may be unpopular, saying "some of my best friends" will support Trump. 
"I just can't go there," he added.
"Maybe I'm the outlier here, probably am. There will be Democrats that can't support Hillary Clinton," Graham said. 
The South Carolinas senator laughed while discussing the potential for Trump and Ryan working together in the near future after the pair exchanged attacks this week. 
"I hope he and Paul can find a common agenda," Graham said. "We'll see what happens."
However, Graham said Trump's detractors in the party should not not mount a third-party candidacy, as some have suggested doing to derail Trump.
"I would advise people not to go down that road," Graham said. 
He slammed Trump's attempts so far to expand the party's base.
"Eating a taco is probably not going to fix the problems we have with Hispanics," he said.
The senator feuded repeatedly with Trump before and after leaving the GOP race in December. Trump last year gave out Graham's cell phone number after the senator called the businessman a "jackass."

The South Carolina senator said during a speech in Beverly Hills, Calif., this week that the GOP had "lost its way" with Trump, whose foreign policy views he harshly criticized.

— This story was updated at 2:38 p.m.