Later on Friday White House spokeswoman Sarah Huckabee Sanders said at a news briefing that Mr Trump was simply "complimenting a foreign leader on the operations of their healthcare system".
"It's a very good bill right now", Trump said of the GOP plan to overhaul the USA healthcare system.
And support for a nationalized health care plan wasn't just something Trump talked about during his latest campaign for president.
"I think he believes that they have a good healthcare system for Australia", she said. "We have a fantastic relationship, I love Australia, I always have", the AFP news agency quoted Mr Trump as saying.
After the meeting, Turnbull described his relationship with Trump as "more family than formal". Trump, too, said that he enjoyed getting to know Turnbull face to face.
MALCOLM Turnbull has revealed what he discussed with Donald Trump behind closed doors in NY, describing the encounter as "more family than formal".
Relations between the two leaders were strained over President Trump's reluctance to honour a deal to accept up to 1,200 refugees from Australian detention camps.
"Of course the Australians have better healthcare than we do - everybody does", Trump tweeted on a rainy afternoon in New Jersey, where he is staying at his mansion there. But Trump has a long history of supporting universal health-care coverage.
The AHCA barely passed through the House, 217 to 213, on Thursday.
'We're not from Beverly Hills', Ramos warns Atletico
Real Madrid already know that, as Zidane said in press conference, so the best idea is trying to attack and score some goals. Even by their standards, Real are on the verge of completing the most glorious season in the club's decorated history.
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 USA and Australia fought the Japanese.
Together, the United States and Australia are building a more secure and stable world.
Trump effectively praised single-payer with his comments.
"Oh yeah sure", Mr Trump said when asked about the United States accepting refugees held on Manus Island and Nauru.
In his 2000 book, The America We Deserve, Trump wrote: "We must have universal health care".
"I also think the interesting thing will be, as we go forward, to see if the Turnbull government makes announcements about further commitments in the Middle East".
Eyeing a victory, a jubilant Trump tweeted during the vote that, if successful, Republicans would gather for "big press conference at the lovely Rose Garden of the White House" immediately afterwards.
On March 13, the CBO score of an earlier version of the AHCA found that it would raise premiums for the elderly and would result in 24 million fewer Americans having access to health insurance by 2026 than if the ACA was kept in place.