MALCOLM Turnbull has revealed what he discussed with Donald Trump behind closed doors in New York, describing the encounter as “more family than formal”.

The Prime Minister met the US President for the first time face to face on Thursday night aboard the USS Intrepid, docked on the Hudson River.

While Mr Trump admitted during the evening that their first phone call in January “got a little bit testy” over a refugee swap deal, the two insist they are now getting on like a house on fire.

Mr Trump and his wife Melania shared a table with Mr Turnbull and his wife Lucy at an exclusive dinner on board the decommissioned aircraft carrier to mark the 75th anniversary of the Battle of the Coral Sea.

“It was a wonderful, warm evening of thanks and recognition of those veterans, and of course it was great for Lucy and I to meet with the President and Mrs Trump,” Mr Turnbull told reporters at a press conference in New York on Friday.

“That was more family than formal, a very, very warm encounter and a great evening.

“It was an opportunity for us to get to know each other, face-to-face.

“We have backgrounds that are similar in many respects — businessmen that found our way into politics — and we’ve also got a lot of friends in common too.

“So it was a very, very warm, as I said, more family than formal.”

When asked about how Mr Trump compared to his predecessor Barack Obama, Mr Turnbull suggested the alliance between Australia and the US transcended personalities.

“The two presidents are obviously very different men but I have been delighted and honoured to meet with each of them,” he said.

“And the relationship between Australia and the United States, the alliance, is so strong, so enduring. It’s built on millions of people-to-people ties. It is family.”

Away from the glare of the media, the two leaders’ discussion focused on national security, especially the rising tensions with North Korea and the battle against Islamic State in the Middle East.

“We have a very intense engagement with the United States on these matters,” Mr Turnbull said.

“We have the third largest foreign commitment to the battle against ISIL in the Middle East and our forces are working together and integrated intimately, as I saw when I visited our forces in Iraq and Afghanistan in the lead-up to Anzac Day … The co-operation [and] collaboration could not be closer.”

The meeting also touched on the economy, trade, investment and tax.

Speaking to reporters after a meeting with business leaders in Manhattan, Mr Turnbull paid tribute to the veterans of the Battle of the Coral Sea, a crucial battle that halted Japan’s looming invasion in the Pacific during World War II.

“We acknowledged and thanked those great veterans of the Battle of the Coral Sea, that battle where Australian and American sailors and aviators turned the tide of war.

“And to see those men in the Royal Australian Navy and the United States Navy standing there so proud receiving the thanks of everybody in that room and all Australians and Americans for what they did when they were just teenagers — 17, 18 years of age — those guys turned the tide, saved Australia, turned the tide of war and began the return of the United States and her allies — Australia and others — to recapture the territories taken so dramatically by the Japanese in the first part of the war.”

Mr Turnbull said the alliance with the US was built on “almost a century of shared service and sacrifice”.

“From the mud of the Battle of Hamel in 1918 when American forces were led into battle by the great Australian general John Monash to victory — again, another battle that started to turn the tide of war — from then through to the waters of the Coral Sea through to the sands of the Middle East today, Australians and Americans stand shoulder to shoulder in freedom’s cause, today as their parents and grandparents did before them and as we always will.

“We are two nations united by a commitment to shared values — freedom, democracy, the rule of law — values we cherish so much that we will always be prepared to fight for them.”

Mr Turnbull will now head back to Australia to make final preparations for the Federal Budget, which will be handed down on Tuesday.