Turnbull made the speech at the Midwinter Ball fundraiser hosted by the media at Parliament House in Canberra on Wednesday night.
Both the prime minister and opposition leader traditionally give off the record speeches, where they joke about politicians and the press.
Audio of Turnbull’s speech, leaked to Nine’s political editor Laurie Oakes, shows the prime minister doing an unflattering impression of the US president.
“The Donald and I, we are winning and winning in the polls,” Turnbull joked.
“We are winning so much. We are winning like we have never won before. We are winning in the polls, we are.”
He added: “Not the fake polls. Not the fake polls. They’re the ones we’re not winning in. We’re winning in the real polls. You know, the online polls. They are so easy to win. I know that, did you know that? I kind of know that. They are so easy to win. I have this Russian guy. Believe me it’s true. It is true.”
Turnbull also joked about the pair’s famously frosty first phone call when Trump reportedly hung up on the PM. Trump described it as the “the worst call by far” he had made after becoming president.
“It was beautiful,” Turnbull said of the pair’s first face to face meeting, in New York. “It was the most beautiful putting-me-at-ease ever.”
During the May meeting Trump praised Australia’s universal health system Medicare, saying it was better than what the US had to offer.
Trump has previously accused Turnbull of attempting to export “the next Boston bombers” to America through the refugee swap deal negotiated by president Obama. The US president described the agreement, which would see the US take in 1,200 refugees from Australia’s offshore detention centres, as “the worst deal ever”.
On Thursday, Turnbull told 3AW radio’s Tom Elliott he was disappointed protocol was breached and his “good humoured” roast was leaked.
He described his speech as “affectionally lighthearted”, claiming he was the butt of all of his jokes.
“The butt of the jokes was myself,” Turnbull said on Thursday afternoon.
“Not Donald Trump?” Elliott asked.
“I wouldn’t say that,” the PM responded.
Turnbull said the speech was lighthearted, affectionate and good natured.
“We’ve got to have a laugh, you’ve got to lighten up… politics is a stressful business, you’ve got to have a bit of fun.”
The PM joked that instead of comedy, at next year’s ball he’ll read an excerpt from the Budget.
A statement from the US embassy in Australia said Turnbull’s speech was all in good fun.
“We understand that last night’s event is equivalent to our own White House Correspondents’ Dinner. We take this with the good humour it was intended,” the statement said.
Oakes, who who did not attend the dinner, decided to publish the off the record speech because he does not believe reporting should be banned at events hosted by journalists.