Mr. Trump and Mr. Ailes, whom Mr. Trump has called “one of the great geniuses in television history,” had a private lunch last month in New York. (A Fox News spokeswoman, Irena Briganti, said they had known each other for about 25 years and had a cordial relationship.) But Mr. Trump has not reached out to arrange a meeting with Mr. Murdoch, as a number of other Republican candidates have.

Fox News has by no means given Mr. Trump a pass for his remarks about Mr. McCain. On Monday, the host Bill O’Reilly chided Mr. Trump. “He was on a bombing mission, he was shot down, he was tortured,” Mr. O’Reilly said. “Come on, Donald, you know that the way that came off wasn’t correct!”

To which Mr. Trump replied with the closest thing yet to an apology: “Certainly if there was a misunderstanding, I would totally take that back.”

CNN and MSNBC have also devoted hours to Mr. Trump, whose histrionics have been a ratings bonanza. But his treatment by Fox News is much more crucial because of the influence the channel wields among the Republican Party’s base. And Fox News, as the host of the first primary debate on Aug. 6, has set the criterion that the debate will include the top 10 candidates as determined by national polls; Mr. Trump currently tops many polls.

Mr. Ailes, who recently renewed his multiyear contract, enjoys his editorial independence and his position as cable news contrarian. And in Fox News’s serious handling of Mr. Trump so far, longtime associates of Mr. Ailes discern a larger plan.

If the Trump balloon ultimately bursts, they suggested, it could buy time for other Republican contenders to hone their messages and become more seasoned campaigners. Either way, Mr. Ailes benefits with ratings in the meantime.

Ms. Briganti, the Fox News spokeswoman, called any implication that the channel’s coverage of Mr. Trump was a ploy to help the eventual Republican nominee “absolute nonsense, 100 percent untrue and said by someone who clearly doesn’t know Roger.”