US President Donald Trump (left) met with his Australian counterpart, Malcolm Turnbull, this week. The two got off to a bit of a rocky start. Photo/AP
After repeatedly insisting that reports about a fiery first phone call between him and Australian Prime Minister Malcolm Turnbull were "fake news", US President Donald Trump has admitted the call "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 okay. We have had a very good relationship and I am very proud of the relationship."
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."
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 insisting 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.
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 indication about when that might happen.
The two leaders 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 are 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, former Australian prime minister Kevin Rudd, billionaire Gina Rinehart and golfer Greg Norman are also in attendance.
The black-tie gala costs as much as US$150,000 ($218,500) for a full-table reservation.
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.
Security is expected to be high on the agenda during the leaders' talks, with escalating tension in North Korea likely to be discussed.
The meeting is expected to smooth over the relationship between the two countries after the phone-call blow-up in January.
Mr Trump reportedly ended a call with Mr Turnbull abruptly 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 come at a busy time for Mr Turnbull, who is preparing to hand down the Federal Budget on Tuesday.