Australian Prime Minister Malcolm Turnbull said he has a "warm" and "enduring" relationship just a day after a transcript of his January phone call with Trump was leaked to the Washington Post and published.

"As I said, it was a courteous, frank conversation," Turnbull told ABC News. "As President Trump said, we're both adults. I stand up for Australia's interests, he stands up for America's interests. We have a warm relationship. You've seen that with our meeting in New York, you've seen that with our meetings in Hamburg at the G-20."

"We have a good relationship between the president and myself, but above all, the relationship between Australia and the United States is very deep, very enduring and one of mutual support in every field and has been and I believe always will be," he said.

The conversation between Trump and Turnbull had previously been described as contentious, but the transcript of their phone call published by the Washington Post shed more light on the exchange.

"I have had it," Trump told Turnbull in the Jan. 28 call. "I have been making these calls all day, and this is the most unpleasant call all day. [Vladimir] Putin was a more pleasant call. This is ridiculous."

The two world leaders had a heated discussion about an agreement made by former President Barack Obama for the U.S. to accept refugees from Australian detention centers.

"I hate taking these people," Trump told Turnbull. "I guarantee you they are bad. That is why they are in prison right now. They are not going to be Malcolm people who go on to work for the local milk people."

Leaks of the transcripts led to criticism from Republicans and Democrats, who agreed they were alarming and dangerous to foreign policy.

Turnbull, too, said he believes discussions between world leaders should be confidential.

"Well, it's always better when these conversations remain confidential," he said. "But I haven't got any further comments to make on it."