When it comes to President Trump, CNN president Jeff Zucker tries not to take the bait.

Trump has made CNN into something of an obsession, incessantly accusing the network of "fake news" despite similar reports coming from many other news outlets. Over the weekend, the president was at it again, accusing CNN of something just short of treason:

.@FoxNews is MUCH more important in the United States than CNN, but outside of the U.S., CNN International is still a major source of (Fake) news, and they represent our Nation to the WORLD very poorly. The outside world does not see the truth from them!

— Donald J. Trump (@realDonaldTrump) November 25, 2017

Yet the president's obsessive attacks on the network, Zucker said in an interview Thursday, Nov. 30, at Business Insider's Ignition conference, aren't distracting its journalists from doing their jobs.

"He is a terrible media critic," Zucker told BI advertising editor Mike Shields. "We're enormous in the U.S."

CNN, Zucker countered, is enjoying the most-watched year in its 37-year history. In terms of digital platforms, Zucker said CNN is the country's most-consumed news and information service. "More people touch us through digital and TV than any other news organization there is," he said.

Yet Trump's fixation on CNN has put a spotlight on the network even as The New York Times, The Washington Post, Politico and others have done similar and, in some cases, harder-hitting exposés of the president and his closest advisers. That's created a two-edged sword whereby CNN's work has greater prominence and greater scrutiny.

It's also cast the network as a potential reason that the the Department of Justice decided last week to sue to block AT&T Inc.'s (T) acquisition of CNN's parent, Time Warner Inc. (TWX) . Whether that's true or not, Zucker said, is well outside the network's control.

"At CNN, even though we are part of the stories in this, it's not something that impacts or affects us at all," Zucker said. "We're doing our jobs. We work for Time Warner now, and if we work for AT&T, so be it. Who we're working for is not something we spend, frankly, any time thinking about, any time."

The Trump presidency, Zucker acknowledged, has been very good for the news business. Like CNN, The New York Times, Washington Post, CBS, NBC and others are breaking revenue, subscription and viewership records.

Over the past few years, though, the acceleration in cord-cutting among pay-TV subscribers prompted CNN to look for ways to broaden its mission beyond breaking news. The network, he said, invested in its digital platforms as well as the making of original series such as "Anthony Bourdain: Parts Unknown," documentaries and other films. 

"We didn't expect this kind of news bump, interest -- I don't think any news organization did," Zucker said. "But we've been evolving the business in anticipation of a continuing lessening of audience. We thought we were preparing for a different world. We could never have anticipated the audience levels we are seeing now."

Zucker concluded, "The one thing I know is that Donald Trump has made American journalism great again."