Pressure continues to build on the Morrison government, even within its own ranks, to free the Tamil family from detention on Christmas Island and back into the Biloela community in Queensland.
Liberal backbencher Katie Allen has joined a small, but growing number of coalition MPs who want them returned to the mainland.
"This has gone on for too long," Dr Allen tweeted on Sunday.
"We urgently need a timely resolution to a situation that is endangering the health and well-being of innocent children."
But acting Prime Minister Michael McCormack has led a chorus of ministers in recent days who say they don't want to encourage the return of refugee boats seeking asylum.
The family's younger daughter Tharnicaa, who turned four on Saturday, remains in a Perth hospital after being evacuated from Christmas Island for medical treatment earlier this week.
Greens leader Adam Bandt said the government's refugee policy is based on "systematic cruelty" towards people seeking Australia's help.
"We are in this situation where this young girl had to be transferred to hospital in a very serious condition because of offshore detention," Mr Bandt told the ABC's Insiders program.
The children in this case were born in Australia and Mr Bandt believes they should be able to stay.
"But we need a broader rethink," he said.
"What this particular case has shown is Australia's refugee policy, backed by Liberals and Labor, is based on putting people like this in effective prisons."
He said an asylum seeker should be able to come to Australia, and have their claim assessed while living in the community, not in detention.
"If they came here again today, both Liberal and Labor would send them offshore and we would be back having this debate time after time after time again and we need to end mandatory detention," he said.
Meanwhile, the Royal Australasian College of Physicians has released an open letter signed by nine separate medical organisations to Home Affairs Minister Karen Andrews calling for an urgent release of the family.
"We know that Australia's detention program is harmful to the physical and mental health of those held, especially children," acting RACP president and paediatrician Jacqueline Small said.
"We want the Australian Government to listen to what medical experts have been saying for years now, that Australia must also release all asylum seekers from detention facilities and provide them with support they will need for this transition."
Dr Small said being held in detention presents an extreme and unacceptable risk to children's health, development and mental health.
"These risks are particularly high for infants and toddlers held in detention. If detention is prolonged, the consequences may be long term or permanent," she said.
