In July, FBI Director James B. Comey said that his agency would not recommend criminal charges against Clinton, but that she and her staff were "very careless" in their handling of classified information.
Trump has made Clinton's use of email a central issue on the campaign trail.
"We're going to get a special prosecutor and we're going to look into it," he said.
Clinton did not directly respond, but again apologized for her use of a private server.
"That was a mistake and I take responsibility," she said.
Clinton said there is "no evidence" that anyone hacked the server and no evidence that classified material ended up in the wrong hands.