Donald Trump said allowing some refugees currently held on Manus island and Nauru would kill him politically. Photograph: Jonathan Ernst/Reuters

Donald Trump told the Australian prime minister, Malcolm Turnbull, that a deal to admit to the US refugees currently held on Manus island and Nauru was stupid and would kill him politically, given his status as the worlds greatest person that does not want to let people into the country.

A White House transcript of the contentious 28 January phone call was published by the Washington Post on Thursday. The Post also published a transcript of a 27 January conversation with the Mexican president, Enrique Pea Nieto, in which Trump seems to dismiss his much-vaunted border wall as a political ploy and asks Pea Nieto not to state publicly that he will not pay for it.

The published transcript showed that in the Turnbull call, which was previously reported to have become angry in tone, Trump complained about the domestic political consequences of the Obama-era Nauru agreement.

Referring to the first iteration of his controversial travel ban on seven Muslim-majority countries, Trump said: I just called for a total ban on Syria and from many different countries from where there is terror, and extreme vetting for everyone else and somebody told me yesterday that close to 2,000 people are coming [from Manus island and Nauru] who are really probably troublesome.

And I am saying, Boy, that will make us look awfully bad. 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.

Turnbull explained, repeatedly, that the US was only obligated to look at taking 1,250-2,000 basically economic refugees from Iran, Pakistan, and Afghanistan, and that Australia had committed to actions in return.

I think we should respect deals, he said.

Why havent you let them out? Trump asked. Why have you not let them into your society?

OK, said Turnbull, I will explain why. It is not because they are bad people. It is because in order to stop people smugglers, we had to deprive them of the product. So we said if you try to come to Australia by boat, even if we think you are the best person in the world, even if you are a Noble [sic] Prize-winning genius, we will not let you in. Because the problem with the people

Trump interjected, to say: That is a good idea. We should do that too. You are worse than I am.

OK, this shows me to be a dope. I am not like this but if I have to do it I will do it but I do not like this at all

The US president continued however to complain and to misstate the terms of the deal as stated by Turnbull, saying: This is going to kill me. I am the worlds 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. It makes me look so bad and I have only been here a week.

The president even linked the agreement to his election win, saying: Look, I do not know how you got them to sign a deal like this, but that is how they lost the election. They said I had no way to 270 [electoral college votes] and I got 306.

Hillary Clinton won the popular vote by more than 2.5m ballots.

That is why [the Democrats] lost the election, Trump repeated, because of stupid deals like this. You have brokered many a stupid deal in business and I respect you, but I guarantee that you broke many a stupid deal. This is a stupid deal. This deal will make me look terrible.

Turnbull insisted on the importance of the US honoring its commitments and said the deal was consistent with the principles set out in the Trump travel ban.

The president yielded, if grudgingly. OK, he said, this shows me to be a dope. I am not like this but if I have to do it I will do it but I do not like this at all.

Trump then complained again and asked Turnbull for a guarantee that anyone admitted would not become the Boston bomber in five years.

Before ending the call, he said: I have had it. I have been making these calls all day and this is the most unpleasant call all day. [Russian president Vladimir] Putin was a pleasant call. This is ridiculous.

The conversation had begun pleasantly enough, with small talk about the Australian golfer Greg Norman, a mutual friend who had given Trumps number to Turnbull.

In subsequent days, Trump returned to the subject. On 2 February, for example, he tweeted: Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!

The US commitment to take the refugees remains unclear.

At the end of the call, Turnbull asked Trump: Do you want to talk about Syria and [North Korea]?

Trump answered with a remark transcribed as inaudible and said: This is crazy.

Thank you for your commitment, said Turnbull. It is very important to us.

It is important to you and it is embarrassing to me, Trump said. It is an embarrassment to me, but at least I got you off the hook. So you put me back on the hook.

You can count on me, said Turnbull. I will be there again and again.

In February Trump tweeted that reports that the conversation had been anything but civil were fake news.

He repeated the claim when Turnbull went to New York in May. In a joint media appearance, Turnbull agreed after Trump said: We had a good call. You guys exaggerated that call, that was a big exaggeration. We had a great call. I mean, were not babies, but we had a great call. That was a bit of fake news.

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