While Fox News continues to promote and defend Donald Trump's presidential campaign, other parts of Rupert Murdoch's media empire and Murdoch himself have criticized the candidate in what appears to be an internal proxy war.

New York magazine's Gabriel Sherman reports that the divergent tone in coverage of Trump's campaign may be evidence of a split between Murdoch and Fox News chairman and CEO Roger Ailes, who recently signed a new contract that will extend his tenure beyond the 2016 election.

Sherman reports that Fox “insiders” say Ailes “is pushing Fox to defend Trump's most outlandish comments.” Trump has called Mexican immigrants “rapists” and criminals, and attacked Sen. John McCain's military record -- remarks that many on Fox have defended. Sherman also reports that Ailes told his senior executives that Murdoch asked him to “back off the Trump coverage” and that in response Ailes told his superior that he would cover Trump “the way he wanted to.”

A Sherman source indicated that “Ailes has instructed The Five co-host Eric Bolling to defend Trump on air.” Bolling recently called companies boycotting Trump for his racist remarks “economic terrorists,” and attacked conservative pundits who criticized Trump. Fox News contributor Pat Caddell is also reportedly helping Trump behind the scenes. Sherman notes, “According to a source with direct knowledge, Caddell has been speaking to Trump 'almost every day' about his campaign.”

A New York Times article reported that Murdoch personally does not like Trump, and the feeling is mutual. The Times reports that Murdoch “often described” Trump as a “phony” to his friends, and disagrees with him on immigration. Murdoch said Trump was “wrong” to characterize Mexican immigrants as “rapists,” and tweeted after his anti-McCain remarks, “When is Donald Trump going to stop embarrassing his friends, let alone the whole country?”

The Times reports that despite his past feuds with Murdoch, Trump has “set his sights” on “wooing” Ailes. They note, “his treatment by Fox News is much more crucial because of the influence the channel wields among the Republican Party's base.”

Associates of Ailes told the Times they believe that promoting Trump could be a win-win for Ailes, since “it could buy time for other Republican contenders to hone their messages and become more seasoned campaigners” while Fox ratings benefit from covering the ongoing spectacle of Trump's campaign.

Murdoch's other media properties have gone after Trump in recent days.

The Wall Street Journal wrote an editorial calling Trump a “catastrophe” and noted, “His only discernible principle is the promotion of his personal brand.” The Journal even said, “The conservative media who applaud him are hurting the cause.” But they didn't mention Fox News.

Trump pushed back against the Journal by writing, “Look how small the pages have become @WSJ. Looks like a tabloid--saving money I assume!” Trump also said, “The ever dwindling @WSJ which is worth about 1/10 of what it was purchased for, is always hitting me politically. Who cares!"

The Murdoch-owned New York Post covered the McCain story with a front page that said Trump was “toast,” adding, “DON VOYAGE!”

Trump has used his Twitter account to amplify criticism from his supporters targeting Fox News, including one tweet directed at the network that read, “tell your owner Murdoch we are turning Fox off if he keeps belittling @realDonaldTrump. No Fox!” Another post he promoted accused Fox of trying to “push Jeb on their viewers.”

Overall, Trump's relationship with Fox has been a positive one. He reportedly privately met with Ailes and tops the network for most time given to the 2016 Republican presidential candidates. At a recent campaign event, he praised Fox & Friends, calling co-hosts Brian Kilmeade, Steve Doocy, and Elisabeth Hasselbeck “great people.”