"The deductibles are going to come down".
"We have a failing health care", said Trump.
Mr Trump and Mr Turnbull got off to a rocky start during their first telephone conversation in January, soon after Mr Trump took office.
"I shouldn't say this to our great gentleman and my friend from Australia", Trump said, "because you have better healthcare than we do".
US Senator Bernie Sanders quickly picked up on the remark that came after Trump's new bill passed by a handful of votes. Australia, like almost every other major developed country, has a universal health care system. "I would put forward a comprehensive health care program and fund it with an increase in corporate taxes", he explained at the time. It could also end up raising premiums on sicker people and abolish key protections for people with preexisting convictions.
The Australian government said that the President's decision to make Turnbull wait was "an awesome snub", CNN reported.
Mr Trump also tweeted on Saturday that "everybody" had better health care than the USA, but the system would "soon be great".
The World Health Organization ranked the U.S.as 37th out of 191 countries on a study of overall national health system performance in 2016 - behind Australia, at 32, but well ahead of bottom-tier countries like Sierra Leone, Myanmar and Central African Republic. Before he left the White House on Thursday, however, he hosted a Rose Garden event to applaud passage of the GOP-sponsored House health care law.
Among those on the street were members of the New York State Nurses Association, who chanted: "What do we want?"
After security costs for Trump and his family of about $24 million during the transition and $300,000 a day since then, Congress voted last week to reimburse the city and other local governments for $61 million.
Brendan Thomas-Noone, a research fellow at the United States Studies Center in Sydney, said whether Australians believed Turnbull had been successful in balancing those needs would likely be shaped by the prime minister's future decisions on Australia's commitment to America's various military operations. In 2015, approximately 28.4 million Americans under the age of 65 were uninsured. "He's fully engaged on the House side, I expect him to be fully engaged on the Senate side and make sure that we get the bill that the American people deserve".
"Of course the Australians have better healthcare than we do - everybody does", Trump tweeted.
"Thank you, Mr. President", Sanders continued.