To tumultuous applause from a celebrity-studded audience paying as much as $US150,000-a-table in a cavernous dining room, deep in the bowels of an aircraft carrier moored on the Hudson River, the leaders used a century of shared military adventures to celebrate values and mateship which, they claimed, set their countries apart in the world.

Time will tell, but they seemed to leapfrog diplomatic discomfort that has lingered since that January phone call, in which an irate Trump gave Turnbull the rounds of the kitchen, over a deal struck between Canberra and the outgoing Obama administration for refugees from Nauru and Manus Island to be resettled in the US - by the simple expedient of jointly declaring it to have been fake news.

After such a bleak start to dealings between Trump's Washington and Turnbull's Canberra, the leaders' speeches to the New York gathering even complimented each other.

Turnbull was all historical and scholarly, tracing an arc from the Coral Sea, where more than 600 Australians and Americans died turning back a 1942 push towards Australia by Japan, to shared US-Australian coalition efforts in the Middle East today. Trump, often incoherent at the lectern, had the audience spellbound with gritty accounts of pilots and their derring-do.

Billionaires and stars of sport and film were at the tables on board the USS Intrepid. But outshining them all and winning multiple standing ovations were seven old men - five Aussies and two Americans who actually fought on the Coral Sea. Billed as "heroes of the greatest generation", they included Australians Gordon Johnson, Norm Tame, Derek Holyoake, Bill White and Andrew Robertson.

Imagery and optics for the celebrity bash to mark that first joint US-Australian air and sea effort, were in the eye of the beholder - as an early American aircraft carrier, the decks of the Intrepid are replete with lethal weapons and powerful aircraft; but these days, it's a decommissioned museum piece, firing blanks from fixed moorings on the Hudson River, on the West Side of Manhattan.

But more worrisome for the Turnbull entourage was a risk that his first sit-down with the new president might get bumped from Trump's agenda by a healthcare political drama unfolding in Washington. To have been berated by Trump in January might have been excused as accidental; but then to have their first face-to-face meeting shunted would have been judged in some quarters as recklessness.

So it was a relieved looking Turnbull who sat next to Trump when a press pack was allowed in for five minutes of banter at the start of their meeting - of course, Trump loved Australia; yes, Turnbull understood only too well the challenge Trump faces in getting the numbers to carry his legislation in Congress.

Yup - Trump had come through for Turnbull. Time and venue had been moving feasts through the day, but shortly after 7pm, they sat together for more than 40 minutes, alone save for the last few minutes when instead of the usual army of advisers, they were joined by - their wives!

In the way of such encounters that go well, the talks were described as "very warm, lengthy and productive," but not in the sense that they produced anything more substantial than a Woodstock-ish feeling of mutual love and affection.

They talked security - national, regional and global; North Korea - a threat; and enhanced cooperation - on trade, immigration and their economies. But what they celebrated as they emerged from their tryst was "the extraordinary friendship between their countries and the vital importance of their alliance."

And their welcome of Melania Trump and Lucy Turnbull to the tail end of their meeting was parsed as proof that the bilateral relationship was "family, not just formal".

To the extent that Turnbull disagreed with Trump, it was confined to the subtext of his dinner speech - these are two New World countries whose rich histories go well beyond shared military adventures; and that as a new president of the US, Trump can't afford to indulge his global scepticism in the face of a relationship that is fundamental to the economic and national security of both countries.

Outlining how World War Two had turned on the allied victory on the Coral Sea and weeks later at Midway, Turnbull described "dark days" for Australia: "Japan's next inexorable advance was to seize Port Moresby in New Guinea, from which it would isolate Australia, take us out of the war, to be invaded as and when it suited the convenience of the new masters of the Pacific."

"But with unity of purpose, unity of command, shared and collaborative signals intelligence, the Battle of the Coral Sea took to the water and the sky, [with] the mateship that had fought and won the [WWI] Battle of Hamel 99 years ago."

Turnbull then explained that in their pre-dinner talks, he and Trump had discussed "the bond our great nations forged in freedom's cause - from the battlefield of Hamel ??? to our forces fighting side-by-side in the Middle East at this very moment."

Here, he argued, was a reminder of how Australia's regional stability and prosperity had been secured for decades and was secured today by the US - "a commitment to the peace stability, the rule of law in our region renewed by President Trump, for which we thank you, sir."

Citing shared values and a shared destiny for the two countries, Turnbull said: "Each of our great nations defines its national identity, not by race or religion or ethnicity as so many others do, but by a commitment to shared political values, as timeless as they are inclusive - freedom, democracy and the rule of law. Fiercely competitive, we always want to win, but we know we are always more assured of winning when we are fighting together.

"We are confident and we trust each other - that is why the United States is the largest foreign investor in Australia and the United States is our largest overseas investment destination."

In reply, Trump ladled on similar sentiment - after an effusive introduction by media mogul Rupert Murdoch. But on the night it was all Australians, not just Rupert, who Trump loved.

Describing Australia and the US as the "rebellious children of the same parent," the President said of his meeting with the Prime Minister: "We reaffirmed the tremendous friendship between the US 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.

"But security also requires friends that you can truly count on, that is why I was pleased to meet with Prime Minister Turnbull ???America and Australia are old friend and really natural partners and with your help, we will remain so for a very, very long time.

"We are proudly and profoundly grateful for Australia's contributions in Syria, Iraq and Afghanistan and their help in the fight against terrorism following the terrible attacks of September 11. On behalf of the US, I thank the Australian people tonight. Believe me, I have so many friends here from this country and we love Australia, all of us, we really love Australia, thank you very much."

Claiming that few peoples shared ties in history, affection and culture, as did Americans and Australians, Trump said: "Those ties were sealed with the blood of our fathers and grandfathers and those same ties are now the priceless heritage we celebrate so beautifully tonight.

"With love for our two nations, with pride in our shared history and with faith in almighty God, we renew our old friendship and we pledge our lasting partnership in the search for prosperity and ever lasting peace. Mr Prime Minister ??? God bless you, God bless our fallen heroes, God bless the Australian people and God bless the United States of America. Thank you, all."

Turnbull was thought unlikely to mention the January phone call before an audience that include the likes of Murdoch, who Trump described as "my great friend"; packaging billionaire Anthony Pratt, who announced a proposed $US2 billion investment which he said would create thousands of jobs in the US Midwest; mall magnate Frank Lowy; former Dow Chemical boss Andrew Liviris; Qantas chairman Leigh Clifford; golfer Greg Norman - on crutches after a mishap on the tennis court; and former prime minister Kevin Rudd, dishing out advice on how Turnbull should handle North Korea and other crises.

Trump did make mention of the January phone call in his speech - conceding after his earlier denials, "It got a little bit testy." Turnbull made no mention of the exchange in his dinner speech, but when both leaders spoke of the call in the banter ahead of their private chat, the Australian leader was quick in identifying by example, a new shared-value.

Asked by Fairfax Media if telephone relations would improve in the future, following a claim by Trump that the Obama refugee deal was "behind us", the leaders had this exchange:

Trump: We had a good telephone call, a great call - you guys exaggerated it. We had a great call - I mean, we're not babies. We had a great call, right?

Turnbull: Young at heart, Donald.

Trump: It was a bit of fake news.

Turnbull: That's exactly right.

Pragmatism and a love-in? As Rick tells the bent cop Renault, as they fade into fog in the closing scene of the movie Casablanca: "Louis, I think this is the beginning of a beautiful friendship."