"If he does attack me, I'll continue to talk about issues. I just really don't buy into the attack-your-fellow-Republicans thing. I'm just not going to do that," Carson said Friday on Bloomberg's "With All Due Respect."
Trump previously said that he would start attacking Carson given the retired neurosurgeon's rise in the polls.
"Probably. At some point, yes, which I actually look forward to doing," Trump said on ABC's "Good Morning America" last week, adding that at the moment, "I can't do it. He's been so nice to me."
And Carson said Friday that the real estate mogul has also been nice to him.
"My personal interactions with him have shown him to be a gentleman," Carson said. "I think there's another element sometimes when he's on camera."
Carson said the biggest issues that differentiate him from Trump are their tax plans and immigration stances. Unlike Trump, Carson is not in favor of deporting undocumented immigrants, but favors a path to legal status.
Carson also believes all residents should pay taxes, whereas Trump wants to exclude the poorest Americans
from having to pay taxes.
The retired neurosurgeon also commented on the Benghazi hearings
, saying that Hillary Clinton was caught "lying." He pointed to the revelation that while senior State Department aides initially told the public that Benghazi was not a terrorist attack, Clinton told family and others in emails that it was.
"I believe she plays fast and loose with the truth," he said.
Carson also blasted Clinton's judgment for using work-related emails on a private server.
"If she doesn't have enough judgment to know better than that, I don't want you to have the keys to everything," he said.