"It's going to be fantastic health care," Trump said, referring to his new health care plan. "I shouldn't say this to our great gentleman and my friend from Australia because you have better health care than we do."
US Senator Bernie Sanders quickly picked up on the remark which came after Trump's new bill passed by a handful of votes.
The new law still has to pass the US Senate.
"Well Mr President, you're right, in Australia and every other major country on Earth they guarantee health care to all people. They don't throw 24 million people off health insurance. So maybe when we get to the Senate we should start off with looking at the Australian health care system," Sanders told CNN's Anderson Cooper.
Australia has a universal health care system, known as Medicare, which gives citizens free access to doctors and public hospitals paid for by the government.
In the US, the new Republican bill will significantly cut the amount of government support
for Medicaid, which provides health care support to some US citizens.
How Australia's health care system works
Australia's health care system is mostly funded by the government while relying on private health insurance for some services.
It was originally introduced by the left-wing government of former Prime Minister Gough Whitlam in 1975
to provide the "most equitable and efficient means of providing health insurance coverage for all Australians." It replaced an earlier system of voluntary health insurance.
Australian residents are able to see doctors and optometrists, as well as receive some minor surgeries, usually free of charge.
The partial cost of pharmaceuticals is also covered under the separate Pharmaceutical Benefits Scheme.
Residents get hospital treatment at no charge, although you can't choose your doctor.
It is partly funded by a 2% levy on all taxpayers, although that can be reduced or even waived
for people earning low incomes.
For the wealthy, an additional tax applies
to people who don't have private health insurance.
In 2014, the Australian government spent 9% of its GDP on health care
, compared to the 17% spent by the United States the same year.
Not everything is free however -- Medicare doesn't cover all dentist visits, most physiotherapy and ambulance services. Many Australians still need private health insurance for some or all of these.
Battle over Obamacare
Health care in the US is much more complicated -- there is no broad overarching government-funded health care system.
Instead, the majority of health care providers are privately run
and health insurance can be purchased to use them.
The vast majority of health insurance is provided by US citizens' employers
, although tens of millions of Americans remain uninsured.
In an attempt to improve the system, former US President Barack Obama passed the Affordable Care Act in 2010, during his first term. A signature achievement of his administration, it came to be known as Obamacare.
It was designed to increase the array of healthcare benefits provided by insurers and levied a tax on the wealthy
to help pay for it. Republicans were strongly opposed to the law and called for its repeal.
However, Democrats say millions of Americans would lose their insurance if Trump's bill was to pass.
The bill also allow insurers to charge higher premiums for those in their 50s and early 60s, compared to younger consumers, and slashes federal support for Medicaid.