A small but growing number of coalition MPs want the Tamil family being detained on Christmas Island returned to what had become their home in Queensland's Biloela.
Medical organisations also want action, saying Australia's detention program is harmful, particularly to children.
The federal government, meanwhile, is expected to make a final decision within days on whether to intervene in the matter and provide visa options for the family.
Liberal backbencher Katie Allen has joined coalition colleagues Trent Zimmerman, Jason Falinski and Ken O'Dowd in wanting the family 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 wellbeing of innocent children."
Family friend and organiser of the "Home to Bilo" group Angela Fredericks said every Liberal or National MP who speaks out provides much-needed hope.
"We welcome every politician who joins the growing call to end this three-year nightmare for Priya and her family," Ms Fredericks said in a statement.
"The safety and wellbeing of a young family is at stake. Now is the time for more than words."
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 federal government is expected to make a final decision within days on whether to intervene in the family's legal battle to stay, AAP understands.
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.
A public vigil was held in Perth on Sunday for the family, expressing support for Tharnicaa and the family's bid to stay in Australia.
"Tharnicaa's health was set up to fail," Australian Medical Association WA president Andrew Miller said on Sunday.
"No child can be raised in a prison-like situation and remain healthy, physically and mentally."
The Royal Australasian College of Physicians has also released an open letter signed by nine separate medical organisations, 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.
"These risks are particularly high for infants and toddlers held in detention. If detention is prolonged, the consequences may be long term or permanent."
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.
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.
Australian Associated Press