Prime Minister Scott Morrison has spoken with Indonesian and Singaporean leaders about the situation in Myanmar.
Hundreds of protesters gathered outside Parliament House in Canberra on Friday to call for an end to the coup in Myanmar.
The protesters want the restoration of the elected government of Aung San Suu Kyi, which was ousted by the military on February 1.
They are also concerned they have been unable to contact family and friends due to a media and internet blackout they say violates human rights.
It is understood Mr Morrison has raised his concerns with at least two of his regional counterparts, Joko Widodo and Lee Hsien Loong.
Foreign Minister Marise Payne has also spoken to her British, Indonesian and Indian counterparts
Labor frontbencher Andrew Leigh, who addressed the Canberra rally, said the government needed to review Australia's defence cooperation program unless democracy is restored.
A petition has been launched calling on Australia to deploy its military to Myanmar in a bid to restore the government.
Australian economics adviser Sean Turnell was among those detained since the military seized power.
Senator Payne confirmed on Friday Australia's ambassador had spoken with Professor Turnell to discuss his health, welfare and the conditions in which he is being detained.
Work was continuing to secure his release, Senator Payne said.
Prof Turnell's wife Ha Vus said he had made a positive contribution to Myanmar.
"He worked for Myanmar by using his knowledge of economic from 20 years. He is someone who brings job opportunities and jobs to Myanmar people."
The Department of Foreign Affairs and Trade said in a travel advisory on Friday there was a risk of further detentions, and warned of limited flights departing Yangon.
The government is exempting Australians returning from Myanmar from the requirement to get a pre-departure COVID-19 test.