"I've come to the point now where I can't go where he's taking the party or the country," the South Carolina Republican told CNN. "He's getting better. You know I hope that he will continue to get better." 
Graham has been one of Trump's most outspoken critics within the Senate GOP caucus. 
He announced in May that he could not support the businessman — despite signing a pledge during his own failed presidential bid that he would back the eventual nominee. He's also repeatedly predicted that Trump will lose. 
Questioned about the areas in which he believes Trump is getting better, he pointed to Indiana Gov. Mike PenceMichael (Mike) Richard PenceTrump attacks Pence aide who called Ukraine call 'inappropriate' Top Pence aide told lawmakers Trump's Ukraine call was 'inappropriate' in closed-door testimony READ: Foreign service officer Jennifer Williams's closed-door testimony from the House impeachment inquiry MORE's support during the vice presidential debate for using airstrikes against the Assad government if Russia doesn't drop its support for the Syrian government's siege against Aleppo. 
Trump has previously ruled out using force against the Syrian government. Pressed about the split within the GOP ticket, Graham added Thursday, "I'm assuming it's Donald Trump's idea." 
Graham has repeatedly pushed the Obama administration to increase its military efforts to fight Syrian President Bashar al-Assad as part of the U.S. effort to end the country's civil war.