The PM was speaking to Canberra's press gallery last night at Parliament House's Mid-Winter Ball.
In his tongue-in-cheek address, Turnbull also poked fun at his own poor ratings in national opinion polls, drawing a comparison to Trump, whose historically dire approval ratings have dogged the first months of his administration.
"Donald and I, we are winning and winning in the polls". Not the fake polls, not the fake polls, not the fake polls! Not the fake polls!
We are winning so much.
"We are winning... not in the fake polls".
"You know the online polls. they are so easy to win". They are so easy to win. I know that, did you know that?
To more laughter, he then added: "I have this Russian guy. Believe me, it's true".
Unchanged India set for Trophy semi-final
You know, no one takes any opposition for granted, and Bangladesh have taken huge strides", Kohli complimented. We will use whatever momentum we've gained in this tournament to execute what we want to.
"(It was) light-hearted, affectionately light-hearted", he said.
He said: "It's a breach of protocol, it's a breach of faith and all those things, but it's light-hearted, affectionate, good natured. It was fun, we've got to lighten up".
The veteran political journalist who reported the speech, Laurie Oakes, said he did not attend the ball and did not accept reporting should be banned at a function hosted by journalists.
Trump and Turnbull met briefly in NY in May on the deck of a United States aircraft carrier, where the U.S. leader said their relationship was "fantastic".
The Australian Prime Minister was reportedly kept waiting around three hours ahead of the meeting.
Malcolm Turnbull's next phone call with Donald Trump could be awkward.
In that phone call, the two spoke about a refugee swap deal between the two countries secured by the administration of former United States president Barack Obama. "That was an exaggeration", he said.
No word yet on if this means we are going to with America yet - but knowing Trump's ego, I wouldn't be surprised if the U.S. defence forces based in Darwin start pulling out the big guns... We had a great call.
He also said the refugee deal had "all worked out".
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