"There are ongoing tensions between the Fiji government and the Fiji military forces and the possibility of a military coup against the government," said an Australian government travel advisory issues on Monday.
"Political tensions could lead to mob violence and civil disorder."
Australian visitors already in Fiji were urged to consider leaving.
Last week Bainimarama issued the government with a list of non-negotiable demands and said it had two weeks to comply.
He also recalled army reserves in preparation for what he called a "clean up" of the government.
Small bands of armed soldiers patrolled the streets of the capital, Suva, on Monday, while others dressed in camouflage uniforms guarded the president’s residence.
Andrew Hughes, the head of Fiji's police has warned that the likelihood of the country being hit by a fourth coup in 20 years has become "too close for comfort".
With tensions escalating, New Zealand has shut its high commission in Suva and moved its staff to the sugar and tourism hub of Nadi.
Australia has ordered naval ships near to Fiji should it need to evacuate its citizens.
"I think a coup is very likely to occur," Alexander Downer, the Australian foreign minister, told ABC radio.
"I think it's going to be very difficult to stop him," he said, referring to Bainimarama.
Downer said he had spoken to Qarase to organize a meeting of South Pacific foreign ministers in hopes of reaching a diplomatic solution to the standoff.
He said the meeting was likely to take place toward the end of the week.
Bainimarama, who is on a visit to New Zealand, has rejected the idea of a third country brokering a compromise.
"My intention of removing this government is clear,'' Bainimarama was quoted as saying on Sunday by the news portal fijilive.com.