Former Immigration Minister Scott Morrison claims softening the government's asylum seeker policy to allow a hospitalised baby to stay in Australia would send an open invitation to people smugglers.
Twelve-month-old Asha remains in the Lady Cilento Children's Hospital in Brisbane after being admitted last month for treatment for accidental burns from boiling water in detention on Nauru.
She has since recovered but is being held by medical staff until "a suitable home environment is identified".
While current Immigration Minister Peter Dutton has been tight-lipped, Mr Morrison says the government will continue to hold its line, "absolutely, completely".
"The risk of departing from the policy in any way, shape or form basically sends an invitation for the trade to recommence," Mr Morrison said on Monday.
Prime Minister Malcolm Turnbull declined to comment on the girl but said "no decision would be taken which would imperil the health or security of any individual".
"We're managing this policy with great care and with great compassion," he said.
Children's Health Queensland executive director Dr Andrew Hallahan confirmed Asha was still being treated in the burns unit at the hospital but talks were occurring about her next move.
Responding to claims sick children would be turned away because doctors won't discharge the girl, Mr Hallahan said the unit wasn't full and beds were available.
"Children's Health Queensland is in discussions with relevant agencies to identify the most appropriate options for the ongoing welfare of the child," he said.
Asha's mother has been staying with her in the hospital while her father, who has been visiting daily, is being detained at Pinkenba, north of Brisbane.
Mark Gillespie, from the Refugee Action Collective, said Asha's father was suffering mental health issues due to the conditions on Nauru and over fears of being sent back.
"The father is absolutely stressed out and worried about going back to Nauru and he was just an absolute bundle of nerves and when I spoke to him," he told AAP.
Mr Gillespie said the accident happened because the family was being housed in a cramped tent where they were forced to boil water for the child's formula.
He claimed the government was acting like "Mr Toughguy" in order to get votes and should increase its refugee quota.
"Finding an alternative pathway so people don't have to get on boats would be a much better outcome," he said.
Mr Gillespie said protesters would continue to hold a vigil outside Lady Cilento for as long as took for authorities to throw Asha and her family a lifeline.
Queensland's premier and health minister, as well as the Royal Australasian College of Physicians, have thrown their support behind the doctors.
However, Opposition Leader Lawrence Springborg said patients who were well and healthy should be discharged.
