President Trump’s nonstop “fake news” trash-talking has taken a heavy toll on the media’s image, with less than 10 percent of Republicans saying they trust the press, according to a new survey.

While the news media feasts on the president and the tsunami of scandals around him, Trump’s war on the press remains effective as his loyal followers still have zero faith in the fourth estate.

While 55 percent of Democrats say the news media “deal fairly with all sides,” less than 10 percent of Republicans feel the same, according to the Poynter Institute’s latest Media Trust Survey.

As the press reels from Trump hammering them as “enemies of the people” — the survey found 31 percent of people agree with this contentious, absurd claim — there is a bright spot for local reporters.

The survey found 76 percent of Americans have a “great deal” or a “fair amount” of trust in their local TV news and 73 percent for local newspapers. But only 59 percent feel that way about national newspapers, 55 percent for network news and 47 percent for online media.

“People overall are pretty critical of the national media and more trusting of their local sources or like them better,” said Rick Edmonds, a media business analyst for the Poynter Institute, a journalism think-tank in Florida.

“And then we take Republicans,” Edmonds said yesterday. “It’s just an enormous gap. They don’t like the national media at all, broadcast and newspapers, but they have a lot of confidence, almost as much as Democrats, in local.”

“As a whole,” the authors of the July report wrote, “the public supports the press, though perhaps only tepidly.”

There’s another bright spot. Americans’ trust of the news media is on the rise, with 54 percent of Americans having a “great deal” or “fair amount” of trust in the press, and that’s up 32 percent from 2016.

The survey found 66 percent of people believe news organizations “keep political leaders from doing things that shouldn’t be done.”

Yet 68 percent of people say the news media “tend to favor one side.”

“We may think we’re straight shooters but our audiences don’t necessarily,” said Edmonds.

The media has some work to do.

Some newspaper editorial page editors have changed how they do things, Edmonds said, including being more engaged in the community and “dialing way back on telling people what they ought to think.”

“Many steps like that will help regain trust,” Edmonds said.

So what about gaining the trust of Republicans?

Keep on doing a solid job, Edmonds said.

“That’s our job,” he added, “to hold people accountable.”