The leaders had some common ground, both slamming the open door policy in Germany on refugees.
In the call with Turnbull, Trump complains about an agreement between the United States and Australia negotiated by former President Barack Obama that would admit 1,250 refugees in Australia to the USA after security screening.
"I hate taking these people", Trump said, according to the transcript, the Post reported.
When Mr Turnbull asked Mr Trump if he would like to discuss Syria or North Korea, the President responded: "This is crazy".
On Wednesday, The Washington Post published the transcript of a January 28 call in which Trump grew increasingly angry over the prospect of accepting 1,250 refugees housed by Australia, a deal that was agreed to by former President Barack Obama.
In a similar exchange, he told Mr Trump: "You can certainly say that it was not a deal that you would have done, but you are going to stick with it".
"This is going to kill me", he said to Turnbull on January 27 during a conversation he described as "the worst call by far" during his nascent presidency, the Washington Post reported, citing a transcript. It is entirely up to you.
He goes on to say that after speaking to Russian President Vladimir Putin (listed first), German Chancellor Angela Merkel, and Japanese Prime Minister Shinzo Abe, " this was my most unpleasant call..." "As far as I am concerned, that is enough, Malcolm. 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". "It is an embarrassment to the United States of America ... this is the most unpleasant call all day".
Trump and Australian Prime Minister Malcolm Turnbull spoke by phone for twenty-five minutes today.
"They are not going to be wonderful people who go on to work for the local milk people", Trump said, seemingly a reference to the massive USA dairy industry. "You are worse than I am".
He then went on to make clear that "Putin was a pleasant call".
Describing the refugee deal once more, Mr Trump said: "It is important to you and it is embarrassing to me".
Mr Trump then said: "Well, it is close".
Turnbull replied: "That is the point I have been trying to make".
Well, you just heard his spokesman said we had a very cordial conversation."So you put me back on the hook".
While Mr Trump quickly denounced those reports as "fake news", these latest transcripts detail the frosty nature of the call. "I will be there again and again".
The US president acknowledged the domestic political difficulties of the issue for Pena Nieto and said a "formula" could be worked out for funding the wall along the southern US border with Mexico.