Just when you thought the President Trump-CNN feud couldn’t get any hotter, both sides on Thursday took a blowtorch to the blowup.

Speaking at a White House press conference, Trump answered a question from a broadcast network reporter about government agency leaks by bringing up the cable news network: “I watch CNN, it’s so much anger and hatred and just the hatred.”

The president also made it personal, telling CNN White House correspondent Jim Acosta to “ask [CNN Worldwide President] Jeff Zucker how he got his job, OK?”

It was not immediately clear what Trump meant.

Meanwhile, Zucker, in New York hosting a long-scheduled media-day event, claimed a recent brand study showed Trump’s constant reference to CNN as “fake news” had not hurt the brand at all.

In fact, Zucker noted, CNN was experiencing a huge ratings bump.

Speaking from the podium at the event, Zucker told reporters they should be concerned about “authoritarian regimes.”

The 51-year-old media bigwig was talking about the Venezuelan government yanking CNN en Español this week after it had reported that the country’s rulers had been illegally selling passports — sometimes to people with ties to terrorism.

The news network’s English-language feed is now under threat of being blacked out, along with access to its YouTube output.

“That’s what happens when an authoritarian regime targets a network because they don’t like our journalism,” Zucker said at the Turner Broadcasting event at the Time Warner Center.

“When an authoritarian regime starts taking down feeds and blocking websites just because we expose the truth … that’s an attack on freedom of the press everywhere,” Zucker said.

Zucker, asked by The Post if he had any direct message for Trump about his fake-news accusations, said, “They have the right to say what they want,” adding that it was clearly part of a “strategy.”

The two men haven’t spoken since late December, Zucker said. Trump was once close to Zucker, the former chief executive of NBCUniversal, when Trump hosted the reality show “The Apprentice.” He is said to believe he was instrumental in helping Zucker get his job at Time Warner-owned CNN.

Zucker also noted that Trump on Feb. 15 had tweeted that CNN was “unwatchable.”

“The only way he knows this is if he’s watching it,” Zucker said.

CNN reporters are not intimidated by criticism and in fact wear it as a “badge of pride,” according to Zucker, who admitted he is a bit concerned about the pace at which news is breaking.

CNN reporters are “exhausted,” said Zucker.

When asked at the press event if he feels responsible for the rise of Trump — from real estate developer to reality TV star to president — Zucker said he does not.

“I put him on a reality TV show 13 years ago,” Zucker said. “That is not why he is president of the United States.”

Zucker is projecting that CNN over the next five years will earn $1 billion from just its digital assets. The network is investing more in coverage of politics from both Russia and Mexico City, he said.

The company is set to begin integration meetings with AT&T, which is trying to acquire Time Warner pending regulatory approval.