An anti-Robert Mueller, anti-FBI fervor is intensifying among Trump supporters -- partly thanks to a campaign by Fox News and other conservative media sources.

The right-wing commentary and President Trump's criticism of the FBI are part of a vicious circle. The TV hosts encourage Trump, then Trump supplies sound bites for their shows, and then the hosts are even more emboldened.

With Mueller's investigation of Russian interference in the 2016 election reaching closer to Trump's inner circle, Fox hosts like Sean Hannity continue to demand Mueller's firing. Every night, Hannity tells millions of viewers that Mueller's probe is a corrupt plot to take down Trump and reverse the outcome of the election. Trump is a big fan of Hannity's show, and the two men speak on a regular basis.

"The anti-Mueller rhetoric in conservative media right now is part of a feedback loop," Nicole Hemmer, the author of a book about conservative media, "Messengers of the Right," told CNNMoney.

"Conservative media personalities know Trump hates the investigation and wants it shut down," she said in an email. "They bash the investigation and Mueller, and when Trump sees that happening (say, on 'Fox & Friends') it reinforces his belief that the investigation is illegitimate and that he should do something to end it. The likely consequence is that this increases the odds of Trump attempting to fire Mueller."

Hemmer added: "We'll have to wait and see whether internal restraints within the White House — lawyers and advisers — are enough to stop him from doing that."

At this point, a loyal viewer of the pro-Trump talk shows on Fox might be frustrated with Trump — frustrated that Mueller hasn't been axed yet.

For more on this story, watch "Reliable Sources" Sunday at 11 a.m. ET on CNN.

For several months, news sources favored by conservatives have been heavily covering every perceived conflict of interest involving the special counsel and every alleged scandal involving the leadership of the FBI.

Many of the storylines revolve around Trump opponents like Hillary Clinton. But some members of Trump's own administration, like Attorney General Jeff Sessions, also come in for scathing criticism. That's why this was a notable comment by Sessions on Friday: "Things that might appear to be bad in the press have more innocent explanations," he told reporters.

He should tell that to TV and radio commentators like Hannity, Laura Ingraham and Mark Levin, all of whom have devoted hours of airtime to anti-Clinton, anti-Mueller and anti-FBI conversations.

That's partly how Peter Strzok became a household name this month. Strzok, an FBI official, helped lead both the Clinton email server investigation and the beginning of the Russian meddling probe. Mueller removed him from the probe when an internal investigation found that Strzok expressed harshly critical opinions of Trump in text messages before Election Day.

Related: How Mueller's path was muddied in two weeks

Strzok is now cited by conservative commentators as a prime example of widespread anti-Trump bias within the special counsel's office, even though he was reassigned.

Some Republican lawmakers have also spoken out forcefully against the FBI. When Deputy Attorney General Rod Rosenstein was questioned on Capitol Hill earlier this week, Hannity played highlights and said, "You've heard it here first. We've been doing this now for months."

That's true. Media Matters for America, a liberal media monitoring group that has urged an ad boycott of Hannity's show, recently estimated that "Hannity and his guests have questioned Mueller's legitimacy or called for Mueller to remove himself or be fired 79 times since the special counsel was appointed."

Hannity sometimes uses propagandistic terms like "head of the snake" and "cesspool" to demean Mueller.

He portrays himself as an investigator out to get the truth about an anti-Trump plot. On Wednesday night's show, he said, "By the time we untangle this massive web of corruption, it will be worse than Watergate. It will be Watergate on human growth hormones and steroids, combined, at massive levels."

Other Fox talk show hosts sing a similar tune. On Thursday night, Laura Ingraham said a "web of Clinton and Obama loyalists" have "burrowed into Mueller's office."

Fox's on-screen banners, social media feeds and web site repeat these messages every day.

One recent segment on Tucker Carlson's show had a banner that asked if Mueller's probe was tainted, while the graphic behind Carlson answered the question: "TAINTED PROBE," it said in bold letters.

On Saturday morning, a banner on "Fox & Friends" asked, "TIME TO INVESTIGATE THE INVESTIGATORS?"

At the same time, the main headline on FoxNews.com asked: "ANTI-TRUMP AGENDA?" The subheadline said "Did the FBI and DOJ plot to clear the way for Clinton and stop Trump?"

Many of the network's guests amplify this conspiratorial point of view. "I think the FBI's been compromised," Judicial Watch president Tom Fitton told Ingraham on Thursday. "Forget about shutting down Mr. Mueller. Do we need to shut down the FBI because it was turned into a KGB-type operation by the Obama administration?"

KGB comparisons have been made on Hannity's show, too. There's been talk about "banana republics" and "third world countries." Jeanine Pirro, a Trump ally who has a weekend show on Fox, has even urged arrests of FBI officials.

"There is a cleansing needed in our FBI and Department of Justice," Pirro said last weekend. "It needs to be cleansed of individuals who should not just be fired, but who need to be taken out in handcuffs."

It's the kind of rhetoric that Trump hears on a regular basis. He claims that Fox News is the only major network news source that's not "fake."

Analysts say he sometimes parrots what he hears on Fox. "It's a shame what happened with the FBI," Trump told reporters on Friday. "It is very sad when you look at those documents," he said, an apparent reference to the text messages.

"You have a lot of angry people that are seeing it. It's a very sad thing to watch," Trump added.

CNN chief legal analyst Jeffrey Toobin reacted this way: "You know who 'a lot of people' are? 'A lot of people' are the people who watch Fox News. Other than that, a lot of people are actually not upset about this investigation. That's shown over and over again in the polls."

But for Hannity, Trump's "angry people" remark reinforced what he's been saying for months. So he played the video clip on Friday night's show.

Elsewhere on TV, Democratic lawmakers have been raising alarms about what they see as an assault against the rule of law.

CNN anchor Wolf Blitzer asked Congressman Jim Himes, Democrat of Connecticut, on Friday, "Do you think these attacks on the FBI, on Robert Mueller, on the Justice Department, are coordinated between the White House and, let's say, some on Fox News and others in the right wing media?"

"Look, no question" there's coordination, Himes said. "Whether there is a hotline between the Oval Office and Fox News -- I doubt that's true. But when the president is talking about the investigation and makes it very clear he wants them over and uses the words 'do something,' you know, people who will sell their souls, who will trade their integrity... will do precisely that."

He called out Hannity, Pirro and "some of my colleagues" on Capitol Hill, meaning the GOP lawmakers who are casting doubt on Mueller's integrity.

In one media universe, Mueller is a man tasked to find out all the facts about Russia's attack on the election. He's a Republican trying to make sure the Republican president didn't break any laws.

But in another media universe, one epitomized by Hannity, Mueller is a "disgrace" who's overseeing a team of "Trump hating, Hillary loving partisan hacks" on a mission to destroy the president.

That's the divide. Pro-Trump media sources are exacerbating the divide every day.

And some observers are hoping against hope that cooler heads will prevail.

Preet Bharara, one of the U.S. attorneys who was fired by Trump earlier this year, tweeted on Friday, "Robert Mueller's attackers are virtually all political operatives and ideologues. They have always been the swamp; he has always been the oasis."

But," he added, "I would caution liberal ideologues also -- he is not your savior; he's just a lawman. Respect his findings, whatever they are."