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…

“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.”