The Department of Foreign Affairs has updated its travel advice for the US, as Prime Minister Turnbull and Treasurer Scott Morrison are asked to comment on President Trump's immigration ban on people from seven Muslim-majority nations.
Australia's prime minister has told reporters he won't critique every one of the US president's policy decisions.
Malcolm Turnbull has reiterated his and Donald Trump's commitment to secure borders as the fallout from the President Trump's latest executive order continues.
"If others wish to emulate what we're doing, they're welcome to do so," Mr Turnbull said when asked about the United States' immigration ban.
"It is not my job, as prime minister of Australia, to run a commentary on the domestic policies of other countries."
Any Australian citizens affected by the seven-country ban on entering the US would have their situations discussed on a case-by-case basis, according to the prime minister.
"We have a very close relationship with the United States and when we want to engage in discussions of this kind, we do so privately and frankly."
Australia's Department of Foreign Affairs has updated its travel advice for the US to include President Donald Trump's executive order to halt visas for nationals from seven countries, but the impact on dual citizens remains unclear.
The Smartraveller website was updated on January 30 to include the changes to entry requirements from January 27, 2017.
"The US State Department has advised visa issuance to nationals of Iraq, Iran, Libya, Somalia, Sudan, Syria and Yemen has been temporarily suspended following the signing of the Executive Order on Protecting the Nation from Terrorist Attacks by Foreign Nationals on 27 January 2017," it read.
Despite the update, there was no clear advice for Australian citizens who hold passports from the seven listed countries on whether they can still travel to the US using their Australian documents.
The office of the Foreign Affairs Minister Julie Bishop issued a statement yesterday to say it was aware of the suspension and was trying to find out what it meant for Australians born in the seven countries named.
"The Australian embassy in Washington is engaging with US officials on the potential implications of the suspension for Australian travellers, including dual nationals," the spokeswoman said.
"Travellers are advised that visa and other entry and exit conditions can change at short notice. Travellers should contact the nearest embassy or consulate of the United States for the most current information.”
'Rest of the world is catching up': Morrison
Treasurer Scott Morrison defended Mr Trump's executive order.
"They have had an election and the President is implementing what he said he would do," Mr Morrison told 2GB Radio in Sydney.
"The rest of the world would love to have our borders and the way they are secured and the immigration arrangements we have put in place, particularly most recently over the last three or four years.
"We have got a good history around this and really the rest of the world is catching up to Australia now."
But Labor Deputy Leader Tanya Plibersek accused the Federal Government of being "missing in action" on the Trump order.
"I'm not really sure what that means. It would be very important, I think, for the Prime Minister to stand up today and seek clarification on how this will affect Australian citizens and permanent residents," Ms Plibersek told reporters in Sydney.
Leaders of Canada, Britain, France and Germany have criticised the suspension of the US refugee program and visa ban.
On Sunday, during a 25-minute phone call, it is understood President Trump assured Mr Turnbull that he would honour a deal struck with former President Obama for the US to take refugees from Nauru and Manus Island.
That drew praise from Mr Morrison: "They are both business people, aren’t they, they know a deal is a deal. The Prime Minister, I think, has done an excellent job in being able to continue this arrangement."
The Opposition says the US refugee deal remains "shrouded in secrecy".
"It's not clear what the Australian Government has given up or committed to get this deal in the first place," Ms Plibersek said.