Nice little network you have here. Be a shame if anything happened to it.

Jared Kushner, President Donald Trump’s son-in-law and close adviser, met with a senior Time Warner Inc. executive in recent weeks and expressed the administration’s deep concerns about CNN’s news coverage, according to a White House official and other people familiar with the matter.

In a meeting at the White House, Mr. Kushner complained to Gary Ginsberg, executive vice president of corporate marketing and communications at CNN’s parent Time Warner, about what Mr. Kushner feels is unfair coverage slanted against the president, the people said.

The Trump administration’s hostile posture toward the news media, especially CNN, has been evident in the president’s own statements and those of his press secretary and top aides. On Thursday, Mr. Trump lashed into CNN once again at a news conference, calling it “very fake news” with expert commentary that is “almost exclusively anti-Trump.”

But the anti-CNN push isn’t just a public display meant to rally Mr. Trump’s supporters. Behind the scenes, Mr. Kushner, the real-estate scion who until recently owned the New York Observer newspaper, has been pushing the issue with Time Warner executives including CNN Worldwide President Jeff Zucker.

“Our journalism has never been stronger as we continue to hold the administration’s feet to the fire. Those are the facts,” said a CNN spokeswoman.

While the administration is battling a large swath of the media, the fight with CNN has special intrigue because its parent company has a massive piece of business awaiting government approval: a proposed $85.4 billion sale to AT&T Inc. Messrs. Kushner and Ginsberg, who have been friends for a decade and whose discussion covered a variety of issues including Israel and the economy, didn’t discuss the merger in their recent meeting, said the people familiar with the matter.

In the final stretch of the presidential campaign, Mr. Trump said he would block the agreement and singled out the news network in his statement. “AT&T is buying Time Warner, and thus CNN, a deal we will not approve in my administration,” he said. The deal will be reviewed by government agencies including the Justice Department.

Such rhetoric from a presidential then-candidate and meetings such as the one between Messrs. Kushner and Ginsberg are unusual, according to Mark Feldstein, journalism historian at the University of Maryland.

“Lord knows that every president has been angered by their news coverage, going back to George Washington,” said Mr. Feldstein. “But to engage in that kind of bare-knuckled tactics is extraordinary.”

Mr. Kushner has taken issue with specific CNN contributors including Van Jones, a Democrat who served in the Obama administration, and Ana Navarro, a Republican strategist, who have each criticized Mr. Trump in harsh terms, the people familiar with the matter said.

CNN’s panels often include a few Mr. Trump supporters, such as Reagan administration veteran Jeffrey Lord and conservative commentator Kayleigh McEnany, a few critics, and journalists who cover the administration.

A White House official said: “It’s no secret that the President and his team have been critical of CNN’s dishonest coverage of the President both during the campaign and since his inauguration, and it’s obvious their ratings have suffered as a result. FOX on the other hand provides mostly fair, and more complete coverage of the Administration and their ratings have never been better.”

After publication of this article, the White House official told The Wall Street Journal that Mr. Kushner’s discussion of CNN with Mr. Ginsberg was not in-depth. The official also said Mr. Kushner denies specifying panelists by name, and said those complaints date back months to the campaign.

The CNN spokeswoman said, “Once again, the White House has their facts wrong. CNN’s ratings are up 50%.”