What followed was a lampooning from Vermont Senator Bernie Sanders, who suggested the President should use Australia's system as a model in developing the Republicans' replacement to Obamacare.
During the Republican campaign to replace Obamacare they railed against government-funded universal heath-care systems like Australia's.
Sanders also promised that Trump's words wouldn't be forgotten when the Senate takes up the American Health Care Act.
Australia's prime minister on Friday described his first meeting with President Donald Trump as "more family than formal", as the Australian ended a brief visit to NY planned to set the tone of bilateral relations with the Republican administration.
Then he unwisely added, "I shouldn't say this to our great gentleman and my friend from Australia, because you have better health care than we do". "Again, he was complimenting the prime minister and we're focused on a healthcare plan that works here". It's going to be fantastic healthcare.
"The two presidents are obviously very different men", the prime minister told reporters on Friday just before flying back to Australia.
President Trump boards Air Force One before his departure from Andrews Air Force Base in Maryland, Thursday, May 4, 2017.
It's also open for debate whether House Republicans' health care plan will move the US closer to countries like Australia.
"You have better healthcare than we do", Mr Trump said. Australians can also buy private health insurance, which covers private hospitals, specialists and other health services.
Border city, county sue Texas over "sanctuary" law
In addition, this alert applies to all encounters with federal, state, county law enforcement including local police and sheriffs. The term often refers to communities where policies prevent law enforcers from helping enforce federal immigration rules.
Australia's healthcare system has been put at the heart of a tense USA debate, the same day it moved further away from universal coverage.
Mr Trump also tweeted on Saturday that "everybody" had better health care than the U.S., but the system would "soon be great".
Last Friday, Trump chose to stick to the original statement- with an amendment: "Of course the Australians have better healthcare than we do - everybody does", he posted to Twitter.
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.
The AHCA barely passed through the House, 217 to 213, on Thursday.
"Under Obamacare, the Medicaid program here in the U.S. expanded quite a lot", says March.
Australia instituted its universal and government-funded health care programme, Medicare, in 1984.