After Stephen Colbert made an oral-sex joke about President Donald Trump and Russian President Vladimir Putin on his show this week, some furious viewers started a #FireColbert hashtag that trended on Twitter, saying Colbert went too far.

On Thursday, Colbert responded to the growing controversy with a statement. There was something notably missing.

"Welcome to The Late Show. I'm your host, Stephen Colbert. Still? I am still the host? I'm still the host!!" he said triumphantly.

"Now, if you saw my monologue Monday, you know that I was a little upset at Donald Trump for insulting a friend of mine.

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"So at the end of that monologue I had a few choice insults for the President in return. I don't regret that. He, I believe, can take care of himself. I have jokes; he has the launch codes. So, it's a fair fight. So while I would do it again, I would change a few words that were cruder than they needed to be."

In other words, no trace of apology to be found. While acknowledging he could have used a different phrase (one other than "c*** holster"), Colbert doubled down. This shouldn't surprise anyone who has followed his career, particularly when he gets involved in online-fuelled controversies, to which he generally responds with non-apologies and more jokes.

About three years ago, on The Colbert Report, Colbert (in character as an uber-conservative news anchor) did a bit about Redskins owner Dan Snyder's plan to create a Washington Redskins Original Americans Foundation - instead of changing the offensive team name.

"Folks, this move by Dan Snyder inspires me, because my show has frequently come under attack for having a so-called offensive mascot: My beloved character Ching-Chong Ding-Dong," Colbert said. "Offensive or not - not - Ching-Chong is part of the unique heritage of the Colbert Nation that cannot change. But I am willing to show the Asian community that I care - by introducing the Ching-Chong Ding-Dong Foundation for Sensitive to Orientals or Whatever ... and I owe all this sensitivity to Redskins owner Dan Snyder."

Later, the @ColbertReport Twitter account tweeted the last quote, completely out of context ("I am willing to show #Asian community I care by introducing the Ching-Chong Ding-Dong Foundation for Sensitivity to Orientals or Whatever") that didn't illustrate he was making fun of Snyder.

Viewers immediately called Colbert racist, and the hashtag #CancelColbert picked up steam.

Even though the person behind the @ColbertReport account deleted the tweet and apologised - making it clear that the host had nothing to do with that account - Colbert took a different approach. "#CancelColbert - I agree! Just saw @ColbertReport tweet. I share your rage," he tweeted from his personal account. "Who is that, though? I'm @StephenAtHome."

Colbert had faced similar situations before. After people called him transphobic when he made a joke about pink slime ("Our beef now has so many hormones, it's a member of the transgender community"), he declined to offer a real apology, and instead made a "Colbology". "I, Stephen Colbert, apologise to any of my transgender bovine viewers that may have been offended. No matter how you were born, no matter how you identify, I want to be clear that I would be proud to grind you up and eat you," he said.

Sometimes he takes even more creative "apologetic" approaches. In 2007, Colbert proclaimed that Hungarians don't know how to play guitar.

"I have nothing against the Hungarian people themselves ... they just can't play guitar!" Colbert said on The Colbert Report. He continued: "And I don't know why I should have to apologise just because they can't shred," before being interrupted by an incredible guitar riff from the side of the stage, from Hungarian ambassador Andras Simonyi. The audience went wild.

"Stephen, why don't you just say you're sorry?" Simonyi asked, offering to give him a beautiful guitar made in Budapest.

"Well, sir, I will, now that I know there's something in it for me," Colbert declared. "Hungarian people of Hungary: I'm sorry."

When he's not in character, however, Colbert will more easily make an apology. He offered one to Trump, who was a guest on The Late Show in September 2015.

"I want to apologise to you because I have said a few things about you over the years that in polite company, perhaps, are unforgivable," Colbert said. "I hope you'll accept my apology ... is there anybody you'd like to apologise to right now yourself?" Trump looked slightly bewildered. "No," he said, with a laugh.