Still, the meeting amounted to a striking turnaround for candidate and anchor alike. Ms. Kelly, in a recent interview, acknowledged that Mr. Trump’s attacks on her had “gotten very ugly” and started to affect her personal life. “I don’t like putting my kids to bed and having to think about that vitriol,” she told Katie Couric in a public interview in Manhattan last week.

Ms. Kelly has also been candid about the difficulties that the feud has created for Fox News, one of the nation’s most influential news sources among conservative voters. “Fox is placed in a very difficult position because they have one of their lead news anchors under attack, and yet what are they going to do?” she told Ms. Couric. “They can’t ban the presidential front-runner on the Republican side from coming on the channel.”

Fox News has defended Ms. Kelly, at one point accusing Mr. Trump of harboring an “extreme, sick obsession” with her. But the network will face a different environment in the general election, when many viewers may expect the channel’s personalities to show allegiance to the Republican nominee.

Mr. Trump is looking ahead, too. After establishing a bullying, showmanlike approach to campaigning, Mr. Trump is in the midst of overhauling his team’s message and approach as he prepares for a potential general election before a more moderate and diverse electorate.

Mr. Trump recently hired a seasoned political hand, Paul J. Manafort, whose portfolio has grown beyond his original assignment as a delegate wrangler at this summer’s Republican national convention. Now, Mr. Manafort is taking a bigger role in Mr. Trump’s messaging and news media strategy.

This week, Mr. Trump has sought to soften his image — or, in his words, “I will be so presidential you won’t believe it.” The shift, Mr. Trump said Tuesday night, has been urged by his family members, who were sitting next to him as he made the remarks during a live town hall-style event on CNN.

With his wife, Melania, at his side, Mr. Trump radiated a paternal beam as his four grown children attested to his skills as a father and mentor. For home viewers, the message was underscored, intentionally or not, by a prominent Twitter hashtag placed by CNN at the bottom of the screen: #TrumpFamily.