- Graham has publicly refused to endorse the Republican presidential nominee
- But he conceded Trump had been more disciplined until the first presidential debate
Graham, who has publicly refused to endorse Trump said the electoral process could be trusted, despite recent cybersecurity concerns in the aftermath of hacking at organizations like the Democratic National Committee
and of state voter records
"I don't think it's good for democracy to have a major candidate for president doubt the outcome," Graham told CNN's Kate Bolduan and John Berman on "At This Hour." "But being rigged means it's rigged against you and I think Mr. Trump's fate is in his own hands."
He added: "I believe that the country will survive long after I'm gone but the country really is a process and the election process I think we need to respect it rather than create doubt about it. Americans have enough to worry about already. Let's don't suggest the election's rigged."
Graham's comments follow Trump telling The New York Times in September that he would have "to see what happens"
before supporting Clinton if she were to clinch the White House in November. Trump has also frequently told supporters the election's outcome is "rigged" and even asked them to sign up to go to polling sites to watch out for fraud.
Graham conceded Thursday that his party's standard-bearer had been more disciplined until the first presidential debate September 26 and hoped that he would continue "to get better."
In particular, Graham -- who serves on the Senate Committee on Armed Services -- said he backed Trump's running mate Mike Pence's position of establishing a safe zone in the war-torn city of Aleppo, Syria.
"The world is not in a good spot," Graham said. "If (Trump) could explain to the country that 'I'll take it in a new direction,' sort of like Mike Pence did (at the vice presidential debate), he could actually win this thing."