The US president mimicked the UK prime minister, using a pathetic-sounding voice to sniggers from the audience at a private Easter lunch, of which a video has emerged.
Trump said Britain "should be our best" ally but had not been.
It is the latest sideswipe the president has made against Sir Keir over his refusal to let Britain be drawn into the Iran conflict.
Trump has also previously been critical of the UK's aircraft carriers, which he dismissed as "toys" that "aren't the best".
Earlier this week, US Defence Secretary Pete Hegseth rounded on the UK for failing to send warships to the region, saying "Last time I checked there was supposed to be a big, bad Royal Navy that could be prepared to do things like that as well".
Speaking at the White House lunch, Trump said: "I asked (the) UK who should be our best.
"In fact the King is coming over here in two weeks, he's a nice guy, King Charles.
"But should be our best but they weren't our best.
"I said 'You have two, old broken-down aircraft carriers, do you think you could send them over'?"
Impersonating Sir Keir with a weak voice, Trump added: "Ohhh, I'll have to ask my team.
"I said 'You're the prime minister, you don't have to'.
"'No, no, no, I have to ask my team. My team has to meet, we're meeting next week'.
"But the war already started. Next week the war's going to be over … in three days."
The conflict has strained transatlantic tensions, with Trump frequently lambasting Britain and other allies over their reluctance to being drawn into the fighting.
As a result, he has said he is considering whether to pull the United States out of NATO.
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