More than 410,000 Rohingya have been driven out of the country by military forces and into refugee camps at the Bangladeshi border.
The crackdown followed a series of insurgent attacks on police and military posts by Rohingya rebels in the Rakhine state on 25 August.
A top United Nations human rights official described the Myanmar military response as a “textbook example of ethnic cleansing”.
There are reports of military personnel burning entire villages and shooting fleeing civilians.
“The Australian government must urgently work alongside the international community to halt what is justifiably being described as the ethnic cleansing of the Rohingya minority by military forces,” Mr McMillan said.
“We are thankful to the Australian government for the announcement of $5 million in aid to respond to the crisis which will go towards much needed emergency assistance in the region.
“We encourage the government to provide this and any further assistance it can to ensure that those fleeing this tragic situation have access to food, shelter and security for as long as is necessary.”
The Rohingya have been described as one of the most persecuted minorities in the world.
Approximately 1.1 million, mostly Muslim, Rohingya live in Rakhine and they have long been targets of violence and human rights abuses.
They are not recognised as Myanmar citizens, which means their rights to marry, study, travel and access health services are restricted.
Last month, members and supporters of the Rohingya community in Melbourne staged a demonstration outside the Department of Foreign Affairs and Trade office in the Melbourne CBD.
The megaphone-led chanting protesters symbolically smeared blood on their shirts and faces to protest against what they described as ‘genocide’.
Habib, a spokesperson from the Australian Burmese Rohingya Organisation, said the crackdown by the Myanmar military was conducted under the pretence of fighting Rohingya rebels.
“The government is targeting civilians in an attempt to cleanse the population,” Mr Habib said.
“The aim is to clean out the Rohingya population and push them into Bangladeshi territory.”
Despite the escalating crisis, the Australian government continues to offer $25,000 to Rohingya refugees on Manus Island detention centre if they return home.
Up to seven Rohingya men – some recognised as refugees – have agreed to return to Myanmar, where they will face the threat of ethnic persecution.
“Australia must do whatever we can to support those who have fled and who cannot return home,” Mr McMillan said.
“I echo calls from the Grand Mufti of Australia Dr Ibhahim Abu Mohammed for the government to allocate a new quota for the arrival of Rohingya refugees into Australia.
“I call on Uniting Church members to pray for our Rohingya brothers and sisters who are suffering and mourning the loss of lives.
“May peace prevail and replace the hate and violence.”