US Senator Ted Cruz has accused the head of America's broadcast regulator of acting like a mafioso in the suspension of late-night host Jimmy Kimmel - the sharpest attack yet from a conservative Republican on the controversy.

He said Federal Communications Commission (FCC) chairman Brendan Carr's threat to ABC over their comedian's monologue about slain conservative influencer Charlie Kirk was dangerous as hell.

That's right out of Goodfellas, the Texas Republican said, as he affected a mobster's accent.

Other Republicans in Congress have been more muted in their criticism of how the FCC pressed Disney-owned ABC to take action on Kimmel, who was indefinitely suspended on Wednesday.

The row started after Kimmel appeared to suggest in his monologue on Monday night that the alleged gunman charged with murdering Kirk was a Maga Republican, although authorities in Utah have said the suspect was indoctrinated with leftist ideology.

Before ABC's decision, Carr said there would be consequences if Kimmel stayed on air. The FCC chairman said that Kimmel was appearing to directly mislead the American public in his on-air remarks.

On his podcast Verdict with Ted Cruz, the senator emphasised on Friday that he hated what Kimmel said about Kirk, and he is thrilled that he was fired. He also said Carr was a good guy.

But what he [Carr] said there is dangerous as hell. And so he threatens, explicitly, we're going to cancel ABC's licence. We're going to take them off the air so ABC cannot broadcast anymore. He says we can do this the easy way, or we could do this the hard way, yeah. And I got to say that's right out of Goodfellas.

He warned that if the government gets into the business of bans and regulating what the media says that will end up bad for conservatives.

In the Oval Office on Friday, President Donald Trump defended Carr and said I disagree with Ted Cruz, who is ordinarily one of his staunchest allies.

Another Republican Senator, Thom Tillis of North Carolina, told reporters that Cruz was absolutely right in his criticism of Carr.

Senator Jerry Moran, a Republican from Kansas, sounded a note of caution on Thursday, stating, The conservative position is free speech is free speech, and we better be very careful about any lines we cross in diminishing free speech.

South Dakota Senator Mike Rounds said he would approach it as an employer-employee issue.

While Kimmel has not commented publicly about his suspension, his late-night colleagues - including Jon Stewart, Jimmy Fallon and Stephen Colbert - have come out in solidarity.

In the aftermath of Kirk's murder, the Senate passed a resolution to designate 14 October - Kirk's birthday - a day of remembrance. Lawmakers in the US House of Representatives approved it, but nearly 100 Democrats opposed it.

The controversy continues to stir political and cultural debate amidst recent violence, with an ABC affiliate suffering gunfire which police linked to tensions surrounding the Kimmel situation.