Australia has a government-funded health-care system, called Medicare, that exists alongside private insurance. The system is funded in part by taxes, including on the wealthy.
The comments came hours after Republicans in the House narrowly approved legislation to replace the Affordable Care Act.
The version of the American Health Care Act that the House approved has not been evaluated by the Congressional Budget Office, but it is estimated that an earlier version of the bill would raise premiums for older enrollees and would have 24 million fewer people insured.
Trump, after advancing his first major legislative priority, hosted lawmakers in the Rose Garden at the White House to mark the occasion.
Later, speaking to reporters after meeting with Turnbull, Trump praised the bill.
“It's a very good bill right now. Premiums are going to come down substantially,” Trump said. “Deductibles are going to come down. It's going to be fantastic health care. Right now Obamacare is failing.”
Most U.S. conservatives oppose universal, government-funded health care. But Trump has a long history of supporting universal health-care coverage.
In his 2000 book, 'The America We Deserve,” Trump wrote: “We must have universal health care.”
Trump's remarks on Thursday thrilled and amused at least one lawmaker: Sen. Bernie Sanders (I-Vt.), who ran for president as a Democrat during the 2016 campaign on a platform arguing for a universal public option, similar to the system in place in Australia.
When Trump's comments were played during Sanders's appearance on MSNBC, the senator threw his head back with laughter.
“The president has just said it. That's great!” Sanders exclaimed.