The US Federal Communications Commission will look into complaints made against talk show host Stephen Colbert for what some have labelled a homophobic joke about President Donald Trump.

Colbert faced a backlash following the Monday night airing of The Late Show, during which he made numerous jokes about Trump during his opening monologue.

Among them, he said: "The only thing [Trump's] mouth is good for is being Vladimir Putin's c**k holster."

Viewers took to social media to declare Colbert's joke homophobic.

The hashtag #FireColbert began spreading around Twitter, along with calls for people to boycott sponsors of the late-night show.

"I have had a chance to see the clip now and so, as we get complaints, and we've gotten a number of them, we are going to take the facts that we find and we are going to apply the law as it's been set out by the Supreme Court and other courts and we'll take the appropriate action," FCC chairman Ajit Pai told Philadelphia's Talk Radio 1210 WPHT.

Colbert responded to the controversy during his opening monologue on Wednesday, saying he regretted his choice of words but stopped short of an apology.

"So while I would do it again, I would change a few words that were cruder than they needed to be," he said.

"I'm not going to repeat the phrase, but I just want to say for the record, life is short, and anyone who expresses their love for another person, in their own way, is to me, an American hero," he said.

"I think we can all agree on that. I hope even the president and I can agree on that. Nothing else. But, that."