Senior ministers are refusing to soften their hardline stance on a Tamil family detained on Christmas Island despite growing community calls to show compassion.
Three-year-old Tharnicaa remains in a Perth hospital after being evacuated from Christmas Island for medical treatment earlier this week.
Supporters believe the conditions in immigration detention may have contributed to her illness.
More than 500,000 people have signed a petition asking the federal government to allow the Tamil asylum-seeker family to return home to Biloela, Queensland, where they previously lived.
Social Services Minister Anne Ruston deferred questions about the Murugappan family to the immigration and home affairs ministers.
But she also seemed to suggest showing the family leniency would restart the "disgusting sights" seen at the height of the people smuggling trade.
"The Australian government takes our responsibility for the care of anybody that is in our care very, very seriously," Senator Ruston told ABC radio on Friday.
"But we equally take the security of our border very seriously."
Attorney-General Michaelia Cash has also warned of the "consequences of blinking" on border security.
Priya and Nades Murugappan met after fleeing Sri Lanka's civil war by boat in 2012 and 2013.
Tharnicaa and her older sister Kopika were both born in Australia after the couple established themselves in Biloela.
The family has been detained for almost three years as the federal government attempts to deport them from Australia.
Their deportation is being fought in the courts.
Queensland Premier Annastacia Palaszczuk is among those calling for the Biloela family to be released from detention and into the community.
"What's happening to that family is incredibly tragic. They were a family based in Biloela and it's time the federal government made a decision," Ms Palaszczuk said.
Immigration Minister Alex Hawke could allow the family to stay in Australia by granting a visa not reserved for refugees, such as skilled migrant or work permits.
Home Affairs Minister Karen Andrews floated the possibility of resettling the family in the US or New Zealand before walking back the idea.
Australian Associated Press