But the reality TV star, who has insulted Sen. John McCain, Carly Fiorina, Ted Cruz's wife Heidi and Kelly herself on the campaign trail, refused to say what mistakes he's made.
"Absolutely I have regrets. I don't think I want to discuss what they are," Trump said Tuesday night in an interview on Fox. "I could have done things differently, I could have maybe used different language in a couple of instances. Overall I'm very happy with the outcome."
Trump, who criticized McCain for being captured during the Vietnam War and made disparaging comments about former presidential candidate Carly Fiorina's face, said he lashes out when he feels cornered.
"When I'm wounded, I go after people hard," he told Kelly. "I try and unwound myself."
But he said the aggression was a key ingredient in his meteoric rise against Republican rivals, even if it doesn't appear presidential to his critics.
"If I didn’t conduct myself in the way I've done, I don’t think I would have been successful," said Trump. "If I were soft, if I were presidential. In a way it’s a bad word, because there’s nothing wrong with being presidential."
The interview with Kelly was an event in itself because of the feud between the two that has dragged on for months. Trump referred to their dispute as "our little difficulty," though he was the source of many insults. Kelly refrained from responding to them, though officials at Fox News often spoke in her defense.
When Kelly asked him in the interview about his repeated use of the word "bimbo" to describe her, he downplayed the severity of the word.
"Ooh, OK, excuse me," he said. "That's not the most horrible thing. Over your life, you’ve been called a lot worse. Is that right? Wouldn’t you say? You had a life that’s not been that easy."
The interview showed Trump and Kelly interacting cordially and without any antagonism.
During the broadcast, Trump live tweeted to supporters.
The feud between Kelly and Trump goes back to a Republican presidential debate in August during which Kelly challenged the real estate mogul on insulting statements he’s made about women.
Afterward, Trump complained that Kelly treated him unfairly.
“You could see there was blood coming out of her eyes. Blood coming out of her wherever,” he said on CNN.
The dispute flared again in January when Trump skipped a Fox News debate because Kelly was slated to moderate it.
He participated in another debate moderated by Kelly in March but unleashed a fresh attack later on Twitter, saying that she was “highly overrated” and “crazy.” Trump also called for a boycott of her show.
They appeared to bury the hatchet in April after Kelly met with Trump in New York. She said they’d reached a “truce,” which paved the way for tonight’s sit-down interview.
Kelly Chen contributed to this report.