In Thursday's debate, Kelly questioned Trump over his history of offensive statements about women.
Calling in to CNN for a 30-minute interview on Friday night with Don Lemon, Trump hurled insults at Kelly, calling her a "lightweight," and bashed her co-moderators, Chris Wallace and Bret Baier, as well as other Fox talent.
"I just don't respect her as a journalist," Trump said of Kelly. "I have no respect for her. I don't think she's very good. I think she's highly overrated."
Trump said he is considering skipping the next debate hosted by Fox News Channel, scheduled for January in Iowa, because he believes he was treated unfairly by the network's moderators.