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Donald Trump said he was “the world’s greatest person” during a phone conversation with the Australian prime minister, leaked transcripts show.

The US President made the big-headed comment in a call with PM Malcolm Turnbull just one week after taking office in January.

According to the Washington Post, which has seen White House transcripts of the conversation, President Trump wanted to drop a deal agreed by Barack Obama to take in 1,250 refugees from Australia.

It came just after the president had announced his travel ban on travellers from several Muslim-majority countries coming into the US.

President Trump told Australian PM Malcolm Turnbull: “Here I am calling for a ban, where I am not letting anybody in – and we take 2,000 people.

“Really, it looks like 2,000 people that Australia does not want, and I do not blame you by the way, but the United States has become like a dumping ground.”

After Mr Turnbull tries to reason with the US leader, Trump replies: “Malcolm, why is this so important? I do not understand.

“This is going to kill me. I am the world’s greatest person that does not want to let people into the country.

“And now I am agreeing to take 2,000 people, and I agree I can vet them, but that puts me in a bad position.”

He added that his call with the Australian PM – during a string of phone conversations with several world leaders that day – was “my most unpleasant call”.

When Mr Turnbull suggested that standing by Obama’s deal would show Mr Trump as a man who is committed, the president replied: “Ok, this shows me to be a dope.

“We are like a dumping ground for the rest of the world. I look so foolish doing this.

“It is horrible for me. I do not know where they find these people to make these stupid deals. I’m going to get killed on this thing”.

Donald Trump's shakes - in pictures 14 show all Donald Trump's shakes - in pictures 1/14 North Korea's leader Kim Jong-un shakes hands with US President Donald Trump at the start of their historic US-North Korea summit AFP/Getty Images 2/14 North Korea's leader Kim Jong-un shakes hands with US President Donald Trump at the start of their historic US-North Korea summit AFP/Getty Images 3/14 US President Donald Trump shakes hands with North Korea's leader Kim Jong-un as they sit down for their historic US-North Korea summit, at the Capella Hotel on Sentosa island in Singapore AFP/Getty Images 4/14 Mr Trump and Kim shake hands for the cameras before sitting down to sign a document Reuters 5/14 US President Donald Trump shakes hands with North Korea leader Kim Jong-un at the Capella resort on Sentosa AP 6/14 Le Crunch Trump and President Emmanuel Macron shakes hands at the US ambassador's residence, on the sidelines of the NATO summit, in Brussels AFP/Getty Images 7/14 The Hug Swerve Back in 2016, Hillary Clinton swerves a hug from Trump following the first presidential debate AFP/Getty Images 8/14 The Comey Shimmy FBI director James Comey rejects a Donald Trump handshake in favour of a handshake 9/14 The Soft Touch Theresa May shakes hands with Trump in Washington earlier this year Getty Images 10/14 The Power Struggle President Donald Trump reaches to shake hands with Canadian Prime Minister Justin Trudeau in the Oval Office AP 11/14 Donald Trump and Chinese President Xi Jinping AFP/Getty Images 12/14 Donald Trump and Russia's President Vladimir Putin AFP/Getty Images 13/14 US President Barack Obama and President-elect Donald Trump shake hands during a transition planning meeting in the Oval Office at the White House AFP/Getty Images 14/14 Vice president-elect Mike Pence and Republican president-elect Donald Trump shake hands Getty Images 1/14 North Korea's leader Kim Jong-un shakes hands with US President Donald Trump at the start of their historic US-North Korea summit AFP/Getty Images 2/14 North Korea's leader Kim Jong-un shakes hands with US President Donald Trump at the start of their historic US-North Korea summit AFP/Getty Images 3/14 US President Donald Trump shakes hands with North Korea's leader Kim Jong-un as they sit down for their historic US-North Korea summit, at the Capella Hotel on Sentosa island in Singapore AFP/Getty Images 4/14 Mr Trump and Kim shake hands for the cameras before sitting down to sign a document Reuters 5/14 US President Donald Trump shakes hands with North Korea leader Kim Jong-un at the Capella resort on Sentosa AP 6/14 Le Crunch Trump and President Emmanuel Macron shakes hands at the US ambassador's residence, on the sidelines of the NATO summit, in Brussels AFP/Getty Images 7/14 The Hug Swerve Back in 2016, Hillary Clinton swerves a hug from Trump following the first presidential debate AFP/Getty Images 8/14 The Comey Shimmy FBI director James Comey rejects a Donald Trump handshake in favour of a handshake 9/14 The Soft Touch Theresa May shakes hands with Trump in Washington earlier this year Getty Images 10/14 The Power Struggle President Donald Trump reaches to shake hands with Canadian Prime Minister Justin Trudeau in the Oval Office AP 11/14 Donald Trump and Chinese President Xi Jinping AFP/Getty Images 12/14 Donald Trump and Russia's President Vladimir Putin AFP/Getty Images 13/14 US President Barack Obama and President-elect Donald Trump shake hands during a transition planning meeting in the Oval Office at the White House AFP/Getty Images 14/14 Vice president-elect Mike Pence and Republican president-elect Donald Trump shake hands Getty Images

The leaked transcript documents also reveal Mr Trump used his first phone call with the Mexican president, Enrique Peña Nieto, to urge him to stop publicly refusing to pay for the wall.

President Trump, who promised during the election campaign to build a wall along the border and get Mexico to pay for it, told Mexico’s leader: “You cannot say that to the press.

According to the Washington Post, he added: “If you are going to say that Mexico is not going to pay for the wall, then I do not want to meet with you guys anymore because I cannot live with that.”

Today’s phone conversation revelations come as it was announced a grand jury has been assembled in the investigation into Russian meddling in the US election.

According to US media reports of the probe, the inquiry has apparently taken the first step towards possible criminal charges.