In the rarefied world of New York moguls, Rupert Murdoch never thought much of Donald J. Trump.

Mr. Trump’s divorces and marriages sold newspapers, but beyond that, Mr. Murdoch had no time for his bombastic business style and ostentatious demeanor. “Phony” was how Mr. Murdoch often described him to friends.

There was the time Mr. Trump screamed that he would sue for libel after Mr. Murdoch’s New York Post reported that the exclusive Maidstone golf club in East Hampton planned to deny Mr. Trump a membership.

Then there was the awkward aftermath of Mr. Murdoch’s own high-profile divorce from Wendi Deng Murdoch, when Mr. Trump’s daughter Ivanka, unlike many New York society figures, remained loyal to Ms. Deng Murdoch, a close friend.

Now, as Mr. Trump holds on to a first-place position in the polls while being roundly denounced across the political spectrum for harsh statements about Mexican immigrants and for belittling Senator John McCain’s war record, he has already lost the man who controls many of the nation’s most important media organizations.