Donald J. Trump and Megyn Kelly finally talked on Tuesday night about their raucous, contentious history over the last nine months. And it appears that things are all patched up.

“I like our relationship right now,” Mr. Trump said in the interview.

It was a convivial, easygoing interview that was taped more than two weeks ago for Ms. Kelly’s first prime-time special on Fox, “Megyn Kelly Presents.”

Ms. Kelly has not been shy about the purpose of the special: With Barbara Walters retired, she has said that she hopes to fill the vacuum of the prime-time host conducting the must-watch interview. Fox increased the exposure by presenting the show on its broadcast network, not the Fox News cable network, on which Ms. Kelly appears on weeknights.

Ms. Kelly’s contract with Fox News is set to expire in a little more than a year, and it is an open question whether she will stay. She said the prime-time special gave her an opportunity to flex “different muscles.”