"This is an immigration minister who called for preferential treatment of white South African farmers over an increase in intake for Rohingyan refugees," Greens senator Peter Whish-Wilson said in Canberra.
Australia allocated nearly $400,000 of training support in last year's budget to the Myanmar military, a group accused of crimes against humanity.
Since last August, the Myanmar military has been accused of driving more than 700,000 Rohingyan refugees across the border into Bangladesh.
Reports of murder, rape, torture and starvation tactics have led to calls for Myanmar to be taken to the International Criminal Court.
The US and European Union have sanctioned Myanmar military leaders, while the UK has cut ties altogether.
"Australia remains one of the only countries who continue to engage, support and train the Myanmar military," said Amnesty International spokeswoman Diana Sayed.
"We are calling on the Australian government to be on the right side of history in condemning ethnic cleansing in Myanmar and cutting all military ties."
Labor MP Ged Kearney recently returned from a week-long trip to Cox's Bazar in Bangladesh, home to thousands of Rohingyan refugees.
"There is not going to be any solution to this soon," she told protesters.
"The Myanmar government talks of repatriation but we know there can be no repatriation if they are not safe."
Crossbench MP Andrew Wilkie said Australia needed to up the ante when it came to targeted assistance for refugees in Myanmar and Bangladesh.