The US president referred to “Mike Pounce” as he reeled off a list of Republicans in attendance at the party’s annual retreat in Baltimore.
Twitter users were quick to pounce on the error and poke fun at the leader, while memes likening the vice-president to a cat were soon being circulated on social media.
“Mike Pounce sounds like someone who guest MCed a Beastie Boys track,” tweeted historian Kevin Kruse.
“I think Mike Pounce is his Grindr name,” joked comedian Dana Goldberg.
Mr Trump’s verbal slip-up came during a typically meandering speech in which he also mocked Democratic presidential candidate Pete Buttigieg's name, stoked fears about illegal immigrants, and blamed energy efficient light bulbs for making him "look orange".
Referring to his decision to scrap a proposed ban on inefficient light bulbs, the president joked: "People said what's with the light bulb? I said here’s the story, and I looked at it. The bulb that we're being forced to use, number one, to me, most importantly: the light's no good, I always look orange."
Mr Trump announced earlier this month that he was rolling back an Obama-era rule that would have seen the US transition to energy-saving LED bulbs and other low-electricity lighting.
During Thursday night's speech, he also suggested "nobody" lived in the US 25 years ago and told California Republican Kevin McCarthy he was "just like a cow" but "smaller".
He delivered the address at a hotel hosting the 2019 House Republican Conference Member Retreat dinner.