The onslaught has contributed to a foxhole-like mentality inside CNN’s offices, where security measures have been tightened and some hosts have considered abandoning their social media accounts because of abuse. Other employees, like Chris Cuomo, co-anchor of the morning show “New Day,” insist that the scrutiny has only galvanized them further.
“I’m comfortable going to work in Thunderdome every day,” Mr. Cuomo said in an interview, referring to the steel-cage fighting venue of the “Mad Max” movies.
Still, CNN’s troubles have been compounded by a series of recent self-inflicted wounds — not least a high-profile retraction of a sensitive article about one of Mr. Trump’s close allies, which last week led to the forced resignations of three veteran journalists.
That episode came after several other mishaps: The network corrected an inaccurate preview of the testimony of the former F.B.I. director James B. Comey, and it cut ties with two hosts, Kathy Griffin and Reza Aslan, after they issued profane online attacks against Mr. Trump, to the delight of critics who called the attacks proof positive of CNN’s bias.
The day after the three resignations, Mr. Zucker phoned in from London to a companywide conference call, telling employees that the heightened scrutiny meant there could be no room for error.
“My job is to remind everyone that they need to stay focused doing their job,” Mr. Zucker said on Wednesday, brushing off any suggestion that he was rattled. He added: “He’s trying to bully us, and we’re not going to let him intimidate us. You can’t lose your confidence and let that change the way you conduct yourselves.”
Mr. Trump’s allies argue that it is CNN’s conduct that is unbecoming. Starting on last year’s campaign trail, the president and his aides have accused the network of bias and arrogance, an offensive that heated up again in January after CNN reported on the existence of a secret dossier detailing a series of lurid accusations against Mr. Trump. The network’s reporters now routinely joust with Mr. Trump’s press aides, and Jim Acosta, a White House correspondent, recently denounced the administration’s use of off-camera briefings as an affront to American values.
White House advisers have discussed a potential point of leverage over their adversary, a senior administration official said: a pending merger between CNN’s parent company, Time Warner, and AT&T. Mr. Trump’s Justice Department will decide whether to approve the merger, and while analysts say there is little to stop the deal from moving forward, the president’s animus toward CNN remains a wild card.
Mr. Zucker, who was ousted as chief executive of NBCUniversal after that company merged with Comcast, declined to comment on the pending deal, except to say that the merger had not affected his journalistic or management choices. “It’s not something I think about,” he said, adding that he had not discussed the proposed acquisition by AT&T with Jeffrey Bewkes, the chief executive of Time Warner.
One challenge Mr. Zucker has thought about: safety. The level of threats against CNN employees, he said, has spiked this year. Mr. Trump, he said, “has caused us to have to take steps that you wouldn’t think would be necessary because of the actions of the president of the United States.”
On Wednesday, CNN found itself facing another backlash — and additional online threats — after it posted a story about a man who created a version of the wrestling video that was later tweeted by Mr. Trump; it did not identify him but said it reserved the right to do so if he resumed his activities.
Some users on Reddit took that caveat as a threat, and it prompted a hashtag, #CNNBlackmail. CNN said it had only meant to make it clear that it had cut no deal with the subject of the article, though some media critics called it an unusual choice.
For CNN, it was yet another dust-up felt by its 3,500 employees as they pursue day-to-day responsibilities and worry about the usual industry concerns, like ratings. CNN has recently placed third in weekday prime time, behind the more ideologically driven coverage of Fox News and MSNBC.
Mr. Zucker noted that CNN’s total viewership among adults 25 to 54, a key advertising demographic, was the highest in the network’s history. And he said the network was on track to clear more than $1 billion in profit this year.
As for the White House, Mr. Zucker acknowledged that there could be a personal component to the hostility of the president, who disdains any signs of disloyalty. Mr. Zucker hired Mr. Trump to host “The Apprentice” at NBC, and the men were friendly for years. Mr. Trump has claimed credit for Mr. Zucker’s hiring at CNN and seems to view the network’s negative coverage as a form of betrayal.
“Television is his preferred medium,” Mr. Zucker said, asked why the president had zeroed in on his network. “And he knows our viewers can be swayed because they’re not watching Fox or MSNBC” — networks with an ideological bent in prime time.
Mr. Zucker, a former “Today” show producer, is also an experienced showman, and he has shown a knack for seizing on some of his network’s feuds with the administration. He smiled when asked about one recent stunt, in which CNN sent a courtroom sketch artist to illustrate a White House briefing that had been closed to television cameras.
“We got a lot of positive feedback to that,” he said.
That gimmick earned at least one fan at the White House as well. Sean Spicer, the press secretary, whose likeness appears in the sketch, has a copy of the drawing — and he now displays it in his West Wing office.