When President Donald Trump delivered a lengthy "fake news" tirade against critical reporters and the media in general, the Australian prime minister suggested such rhetoric was wrong-headed.

And to prove his point, Malcolm Turnbull used a quote he said was from widely respected British wartime leader Winston Churchill.

"A very great politician, Winston Churchill, once said that politicians complaining about the newspapers is like a sailor complaining about the sea," Turnbull told reporters in New Zealand on Friday when asked about Trump's relationship with the media.

POOL Australian prime minister Malcolm Turnbull made the gaffe at a media stand-up in NZ.

"There's not much point. It's the media we live with, and we have to get our message across, and we thank you all in the media for your kind attention."

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However, Turnbull may have unintentionally undermined his own argument.

REUTERS Winston Churchill never said that politicians complaining about the newspapers is like a sailor complaining about the sea.

But there's no evidence that Churchill ever uttered that phrase or anything like it.

Instead, the quote is widely attributed to another British firebrand of the same era - Enoch Powell, a politician whose name is near-synonymous in Britain with alleged racism due to a speech he gave in 1968 that warned of "rivers of blood" if immigration continued to Britain.

Regardless, the comments appear be the latest round in a back and forth between Trump and Turnbull - an unusual diplomatic disagreement between two traditional allies whose relationship has been shaken since Trump arrived in the White House.

STUFF.CO.NZ Australian Prime Minister Malcolm Turnbull pays tribute to helicopter pilot Steven Askin.

Despite their countries' long friendship, the US president and the Australian prime minister had a tense phone call the week after Trump entered office.

According to US officials briefed on the exchange, Trump had used the call to brag about his election win before turning his ire on a refugee deal between the United States and Australia agreed to under the previous administration.

When Turnbull tried to get reassurances that the deal would still go through, Trump complained that Australia was trying to "export the next Boston bombers" with the "dumb deal."

Trump told Turnbull that the call was "the worst by far" of several he had had with world leaders that day - and abruptly ended the call less than halfway through a planned hour-long conversation.

These reports of the call, at odds with official readouts from both sides, soon sparked widespread controversy and focused attention on Trump's unorthodox discussions with a number of other world leaders.

Trump, seeming to acknowledge the content of the call, later tweeted out further complaints about the refugee deal, while Turnbull offered an oblique acknowledgment that the discussion had been "frank and forthright."

Trump later sent two top advisers to reassure Australia's ambassador that their relationship was still strong.

However, the US president seemed to offer another dig at Turnbull on Thursday, telling reporters that the call "wasn't that important."

Turnbull's relationship with Trump has become a major factor in perceptions of his leadership of Australia.

The Australian prime minister, leader of the centre right Liberal party, has been in office since September 2015.

His government has suffered from low approval ratings, but some suspect that his disagreement with Trump may boost his popularity among Australians, who generally have negative opinions of the US president.

The prime minister's attempted use of a Churchill quote may be notable.

One of the first things Trump did when he entered the White House was return a bust of the British leader to the Oval Office - seemingly a nod to a controversy over reports that President Obama had removed the bust.

(In fact the White House may soon have two busts of Churchill.)

Turnbull's comments also came a day after the Australian newspaper reported that, despite their disagreement, Trump had expressed some admiration for the Australian leader's passion.

"There is a brawler there," the American president is reported to have said after their conversation ended, a US source told the Australian's Simon Benson.