Fox News anchor and political commentator Chris Wallace lectured mainstream media members for “overreacting” to President Donald Trump’s “bait” on Thursday night — then clashed with host Stephen Colbert about whether the media are biased on CBS News’ “The Late Show with Stephen Colbert.”

The late-night TV host, known for his almost-constant anti-Trump rhetoric, asked Wallace to recount the lecture he gave to mainstream media members last week at The Media Institute’s “Free Speech America” gala, at which Wallace received the Freedom of Speech Award.

“Now, you spoke of the media making mistakes covering Trump. What are those mistakes?” Colbert (pictured above right) asked Wallace (above left).

Wallace first noted that he “called out the president” for saying fake news was the “enemy of the people,” which is “unacceptable.”

But then he urged his peers not to take Trump’s “bait.”

“What I then went on to say — and this is where we get to your part — that I do think that the press has made a mistake in some cases in taking the president’s bait and overreacting to it and sometimes playing his game,” Wallace said.

“We are not in his game. We shouldn’t fight fire with fire.”

“His job is to be a disruptor and you want to call him whatever you want to call him — our job is to be reporters, and that means being umpires, calling balls and strikes, being fact checkers, pointing out when things are wrong,” Wallace added.

“But we shouldn’t try to match his invective with our invective.”

Related: Trump Vowed Swift Justice for the Mail Bomb Suspect

Who do you think would win the Presidency?

By completing the poll, you agree to receive emails from LifeZette, occasional offers from our partners and that you've read and agree to our privacy policy and legal statement.

The segment became heated, however, after Wallace offered an example of the media’s bias when it came to their feverish reporting on mail bomb suspect Cesar Sayoc’s support for Trump.

Sayoc was arrested last week for sending a string of suspicious packages containing crude explosive devices to prominent Democrats and to CNN’s New York City bureau.

It didn’t take long for media members to blame Trump for the crimes — even before the suspect’s identity and his support for Trump were revealed — because the targets were all the recipients of the president’s criticism.

“And I’ll give you just one quick example — front page of ‘The Washington Post’ on Saturday the day after Cesar Sayoc, the mail bomb suspect, was caught. I thought the headline, big banner headline was was going to be ‘Mail bomb suspect caught,'” Wallace said — before noting that the headline read something more along the lines of, “Mail bomb suspect: outspoken supporter of Trump.”

“And I’m not saying you can’t report that he had Trump stickers all over the place. It shouldn’t be the lead headline in the story.”

“Do you think that should have been the lead headline in ‘The Washington Post,’ seriously?” Wallace asked Colbert, who replied, “Um, there’s nothing wrong with it.”

“But is that the news?” Wallace pressed further.

“It didn’t even tell you [Sayoc had] been caught.”

Related: Liberal Co-Hosts on ‘The View’ Go After Geraldo; He Refused to Blame Trump for Bomb Threats

Colbert replied, “Well, no, it does tell you he was caught because they found out who he is — because they found out he was a Trump supporter.”

Wallace fired back, “Whitey Bulger was on the run 20 years. We knew who he was.”

The two argued over whether the suspect’s motivation mattered enough to make The Post’s headline in place of other key details.

“It doesn’t matter because he’s a criminal,” Wallace insisted. “What would have happened if he were a Democrat? So therefore, Democrats should hang their heads in shame? He was a psychopath!”

Colbert argued, “The headline doesn’t say ‘Hang your head in shame.’ It describes the person who did it.”

“I understand, but it’s basically giving the president responsibility for what this nut did,” Wallace emphasized.

“And I’m not saying you can’t report that he had Trump stickers all over the place. It shouldn’t be the lead headline in the story.”

Watch more of the tense segment below: