President Donald Trump and Australian Prime Minister Malcolm Turnbull shake hands during their meeting aboard the USS Intrepid.
But the White House has since clarified those comments, saying the US President was simply saying nice things to an ally and did not think his country should adopt a similar approach. Seconds later, Trump added that the call did, in fact, "get a little bit testy".
The president took to Twitter afterward to label the agreement as "dumb", rattling a decades-old alliance.
"It's all worked out".
The tweet was accompanied by a video detailing Australia's medicare system, saying it guarantees better service at half the price of USA healthcare.
"They said we had a rough phone call, we really didn't have a rough call, did we?" That was a big exaggeration.
It's seems depressingly likely, given both the circumstances, and the core of his fugly, orange-colored soul, that Trump might have just been indulging in his usual love of hyperbole and Obamacare-directed shit talking.
"We get along great".
The battle was a turning point in the war and led to an alliance between the U.S. and Australia.
White House officials said the US-Australia refugee deal still stood, but remained a "raw nerve" for Mr Trump. Turnbull travelled to NY for the commemoration of the 75th anniversary of the Battle of the Coral Sea.
Together, the United States and Australia are building a more secure and stable world.
He said North Korea, the Islamic State group and global trade were all discussed.
Trump is set to meet Turnbull on Thursday night here at the Intrepid Naval Museum, a retired US Navy vessel that is anchored on the Hudson River.
"It's great to be with you", Mr Trump told the prime minister.
"Oh, that will happen".
"One of the great, great places", he enthused.
We'll probably never know for sure, but I have a strong hunch that Trump could be talked into endorsing a single-payer system in a matter of minutes.
Trump and Turnbull addressed a black-tie dinner aboard the USS Intrepid to mark the 75th anniversary of a World War II naval battle in the Coral Sea in which the US and Australia fought the Japanese.
Australia has government-funded universal health coverage via a program called Medicare, which allows its citizens to visit doctors and public hospitals for free.
Turnbull highlighted the close military ties between the two countries.
"Our fearless warriors have fought shoulder to shoulder in every major conflict together", he said.