US TV viewers have called on network CBS to fire late night host Stephen Colbert, following a controversial monologue that has seen the host labelled as "homophobic".

Colbert, who took over David Letterman's gig in 2015, has seen the show's ratings claw back against rival Jimmy Fallon with his considered takes on Trump's follies, but his latest monologue went atomic.

In an epic roast filled with insults, the comedian got personal with the president, following Trump's dismissive performance during an interview with Colbert's CBS stablemate John Dickerson, in which Trump referred to Dickerson's Face The Nation news program as "Deface The Nation".

"When you insult one member of the CBS family, you insult us all," Colbert said, before launching into his rapid-fire tirade.

Stephen Colbert has sparked outrage with his latest anti-Trump monologue. CBS

Among the quips were, "Sir, you attract more skinheads than free Rogaine" and "You have more people marching against you than cancer."

But it was another hit that sparked the most controversy: "You talk like a sign language gorilla that got hit in the head," said Colbert. "In fact, the only thing your mouth is good for is being Vladimir Putin's c—k holster."

The joke drew instant rebukes from online commentators, who labelled the quip "vulgar" and "homophobic".

A Twitter campaign demanding CBS sack the host has since gone viral, with the hashtag #FireColbert trending worldwide, as others demanded advertisers cut their relationship with the network.

While criticisms largely came from Trump supporters and conservative commentators, including Republican consultant Karl Rove who took to Fox News to call the host an "SOB", Colbert also drew the ire of LGBTI activists.

"Homophobia for the right cause, with the right targets, is good homophobia, apparently," said journalist Glenn Greenwald, linking to a Daily Beast article which defended the joke.

"For someone like Colbert who typically presents himself as [an] LGBTQ ally, this is not a good thing. It's an expression of systemic homophobia," another commenter added.

CBS have yet to comment on the furore.

Colbert faced similar outrage in 2014 while hosting the Daily Show spin-off The Colbert Report, after a satirical tweet seen as mocking Asian-Americans led to the viral hashtag #CancelColbert.