"You know, I really don't know," he told CNN's Wolf Blitzer on "The Situation Room" when asked who he believed would do a better job.
"At the end of the day, if you're not worried about Donald Trump or Hillary Clinton being president of the United States, you're crazy. Look at both of them," Graham said.
Graham elaborated that he believed Clinton is "naive," adding that Trump is wrong about how to handle the Mideast.
"I think her judgment is very much flawed when it comes to understanding the Mideast," the South Carolinian said. "Donald Trump believes it is better for dictators to be in power rather than support people who want to have more social justice and have more of a Democratic life. I think Mr. Trump, quite frankly, that the young people in the Mideast are not going to live in dictatorships for our convenience anymore."
But Graham, a leading foreign policy hawk on Capitol Hill, also said he preferred Clinton's national security plan over Trump's because he liked the idea of "a safe haven inside of Syria."
"The thing I object to about Donald Trump is that he wants to keep (Syrian President Bashar al-Assad) in power," Graham said. "The one thing I want your viewers to know from my point of view -- you'll never end the war in Syria if you leave Assad in power ... So Mr. Trump, your view that you can solve the war in Syria and end it by leaving Assad in power, I think, is fatally flawed."
Later, Blitzer asked Graham whether Trump owes President Barack Obama an apology for the birther controversy he's fueled.
"I think so," Graham responded. "I don't believe he's a Muslim and I don't believe he was born in Kenya ... If you really do believe this President was born in Kenya, then I'm not so sure I want you to be my President."
Earlier on Wednesday, Indiana Gov. Mike Pence said he believes Obama was born in the US, drawing a clear distinction with his running mate on the issue.
"I believe Barack Obama was born in Hawaii, I accept his birthplace. I just don't know where he's coming from on foreign policy and on economics and on Obamacare," Pence told reporters aboard his campaign plane just after it touched down here.