AFTER repeatedly insisting that reports about a fiery first phone call between him and Malcolm Turnbull were “fake news”, Donald Trump has admitted the conversation “got a little bit testy”.

The two leaders’ relationship got off to a rocky start in January when Mr Trump reportedly scolded Mr Turnbull over a refugee swap deal.

But speaking at an exclusive dinner marking his first face-to-face meeting with the Prime Minister in New York on Thursday night, the US President pointed the finger at the media for exaggerating the story.

“They said we had a rough phone call — we really didn’t have a rough phone call, did we?” Mr Trump said, addressing Mr Turnbull.

“Everyone is talking about this phone call. The media were saying ‘What do you think of the phone call? You didn’t really hang up?’ We had a very nice call, right?

“Now the record is straight. It is true, we had a very nice phone call.

“It got a little bit testy. But that is OK. We have had a very good relationship and I am very proud of the relationship.”

Despite the admission of the early testiness in the relationship, the two leaders appear to have buried the hatchet, with Mr Trump hailing Mr Turnbull as a “very, very special Prime Minister”.

Elsewhere in the official speech, Mr Trump revealed what he and the Prime Minister discussed away from the cameras during their first face-to-face meeting.

“Together, we discussed crucial issues, ranging from national security to trade, to immigration and enhanced economic co-operation,” the President said.

“We reaffirmed the tremendous friendship between the United States and Australia and the vital

importance of our security and our alliance.

“The armed forces of our two nations are operating side-by-side almost every day, fighting to defeat ISIS and the scourge of terrorism.”

The President went on to say: “Americans have had no better friends than the Australians; I mean that.”

Mr Turnbull had strong words for North Korea during his speech.

“Today, together, we condemn and we resist North Korea’s reckless provocation,” the PM said.

“We fight together in Iraq and Afghanistan to defeat and to destroy the terrorists who threaten our way of life.”

The leaders’ notorious call was discussed about an hour earlier at their sometimes-awkward first face-to-face meeting.

While the one-on-one on board the USS Intrepid aircraft carrier was cordial, the conversation did not exactly flow freely.

Mr Trump insisted again that he had a “great call” with Mr Turnbull and that the story was “fake news”.

“We had a good telephone call,” Mr Trump said.

“We had a great call!” Mr Turnbull chimed in.

“You guys exaggerated that call. That was an exaggeration,” Mr Trump told reporters. “We had a great call.

“I mean, we’re not babies.”

“Young at heart, Donald,” Mr Turnbull joked.

Mr Trump spoke of his affection for Australia, as Mr Turnbull looked on.

“We get along great. Always have,” Mr Trump said.

“I love Australia. We have a great relationship,” he added, gesturing towards the PM.

Mr Trump pushed back his first one-on-one meeting with Mr Turnbull after scoring his first big win in Congress.

The two leaders were scheduled to meet for the first time in New York about 4pm on Thursday, US time, but the face-to-face was delayed by about three hours after the US House of Representatives passed a Bill to repeal and replace Barack Obama’s healthcare law, ObamaCare.

The President stayed behind in Washington to celebrate his achievement with a massive Republican press conference at the White House.

Mr Turnbull congratulated Mr Trump on the Bill, explaining how his numbers in the Australian Senate made passing legislation a challenge.

“It was a very big day. I appreciate your waiting,” Mr Trump told Mr Turnbull.

News.com.au understands Mr Trump personally called Mr Turnbull earlier on Thursday to explain that he was dealing with a major piece of legislation — the healthcare bill — and that he looked forward to meeting him that night.

Mr Trump also shed some light on the strategy behind his ubiquitous tweets during the meeting between the two leaders on the aircraft carrier docked in the Hudson River.

“Social media is the way to go,” the President said.

“I have got over 100 million people watching and social media is the way to go.

“This way, if somebody’s not treating you properly or if you do have fake media — not all of it is fake, some of it is fantastic — you can circumvent … It is a fast way of getting the word out.”

Mr Trump also vowed to visit Australia, but did not give an impression about when that might happen.

The two leaders will both gave speeches during the exclusive dinner aboard the USS Intrepid to mark the 75th anniversary of the Battle of the Coral Sea.

Some of the Trump Administration’s biggest names and some of Australia’s richest business people were in attendance at the Intrepid event, hosted by the American Australian Association.

Mr Trump and his wife Melania shared the main table with Mr Turnbull and his wife Lucy, Rupert Murdoch, the executive chairman of News Corp, publisher of news.com.au, Australian ambassador to the US Joe Hockey and his wife Melissa Babbage, Mr Trump’s chief of staff Reince Priebus, Dow Chemical Company chief executive officer Andrew Liveris and Westfield chairman Frank Lowy.

US Secretary of State Rex Tillerson, golfer Greg Norman and Hollywood actor John Travolta were also in attendance.

The black-tie gala costs as much as $US150,000 ($A202,365) for a full-table reservation.

Earlier on Thursday, Mr Turnbull toured the hi-tech New York Police Department Joint Operations Centre, which is tasked with protecting the city from potential terrorism attacks.

The Manhattan headquarters keeps a close eye on the metropolis via more than 10,000 CCTV cameras. The PM said he was “very impressed by the vision”.

Mr Turnbull then walked a few blocks to a federal government building where he met with Admiral Harry Harris, the commander of the US Pacific Command, which works closely with the Australian Navy.

Thursday night’s event was the first time Mr Trump has visited New York, his home town, since his inauguration.

News.com.au saw protesters gathering over the road from the USS Intrepid on Thursday afternoon, some holding a “No Trump in NYC” banner.

The meeting between the two leaders was timed to celebrate an important anniversary to celebrate the ties between the US and Australian militaries.

World War II’s Battle of the Coral Sea, which ran from May 4 to 8, 1942, has been dubbed “the battle that saved Australia”, because it halted Japan’s looming invasion of the country.

The strategic victory is also well remembered because it was a significant joining of US and Australian naval forces to defeat a common enemy.

Mr Trump reportedly ended a call with Mr Turnbull abruptly in early January when the PM urged the President to honour a deal struck with the Obama Administration to take 1250 asylum seekers from Australia.

While both leaders played down the tension, Mr Trump later tweeted that he would “study this dumb deal!”

Thursday’s events also came at a busy time for Mr Turnbull, who is preparing to hand down the Federal Budget on Tuesday.