Stephen Colbert has been vocal on his dislike of US President Donald Trump – having lampooned the man since he entered the presidential race last year. Now it looks like The Late Show host's visceral monologues have finally paid off – with a response from the Potus himself.

Colbert celebrated the fact that after a year of criticising Trump, the president had finally graced him with a mention. "You see a no-talent guy like Colbert. There's nothing funny about what he says. And what he says is filthy," Trump told Time magazine on 8 May. "And you have kids watching. And it only builds up my base. It only helps me, people like him."

Trump went on to claim responsibility for the CBS host's improved ratings, something that Colbert himself has previously acknowledged. "The guy was dying. By the way, they were going to take him off television. Then he started attacking me and he started doing better. But his show was dying," Trump said.

So on 11 May, the former The Daily Show correspondent decided to address the matter in his regular monologue. "The president of the United States has personally come after me and my show... And there's only one thing to say," Colbert began solemnly. "Yayyyy!"

Blowing a kiss to the camera as the audience chanted his name, he addressed the president, explaining that even a bad review made for good publicity. "Mr Trump, there's a lot you don't understand. But I never thought one of those things would be show business," he said. "Don't you know I've been trying for a year to get you to say my name?! And you were very restrained. Admirably restrained.

"But now you did it! I won."

Colbert also responded to Trump's mention of his 1 May monologue in which he went off the rails with a barrage of crude insults directed at the president. "I will give this to the man, you're not wrong. I do occasionally use adult language — and I do it in public instead of the privacy of an 'Access Hollywood' bus," he said to a host of boos from the audience.

He went on to talk about his show's success while mentioning Trump's own falling approval ratings. "But since all of my success is clearly based on talking about you, if you really want to take me down, there's an obvious way," Colbert added. "Resign."