Australian Prime Minister Malcom Turnbull has poked fun at US President Donald Trump by mimicking him, joking about his poll numbers, his attacks on "fake news" and his alleged links to Russia.

Turnbull mocked Trump in a speech on Wednesday night to a gathered crowd of journalists and politicians, during the Australian Parliament's boozy annual Midwinter Ball, CNN reported.

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In leaked audio aired by Australia's Channel Nine, Turnbull poked fun at his own efforts to ingratiate himself with the new US President during their meeting in New York.

"It was beautiful. It was the most beautiful putting-me-at-ease ever," he told the crowd.

The Midwinter Ball is the premier event of the political year in Canberra, a mixing of journalists, advisers and politicians, similar to the White House Correspondents Dinner.

But unlike the US version, Turnbull's speech was supposed to be off the record. However, Channel Nine decided to air it when parts of Turnbull's speech were posted to the social media.

Turnbull's speech, which was also self-deprecating about his own poor opinion poll ratings, showed him impersonating the US President's unique oratorical style.

"The Donald and I, we are winning and winning in the polls. We are winning so much! We are winning like we have never won before. We are! Not the fake polls. They're the ones we're not winning in. We're winning in the real polls," he said.

Turnbull also made fun of Trump's ongoing troubles with allegations of Russian involvement in the 2016 US election.

"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 said.

Speaking in a 3AW radio interview shortly after the speech was leaked, Turnbull said the speech was "light-hearted" and "affectionate".

The Australian Prime Minister and the US President had only just repaired their relationship after a reportedly heated phone call in January over the planned US-Australian refugee deal.

Trump and Turnbull met briefly in New York in May on the deck of a US aircraft carrier, where the US leader said their relationship was "fantastic".