The Prime Minister says his government will not save a Tamil family from deportation because it would expose Australia to a new wave of boat people.
Scott Morrison says granting an exception for a family whose asylum claims had been denied would kick-start the people smuggling trade.
He said the government could not be seen to change its position on the basis of "a public reaction" to the family's plight.
"I know what happens when people think it's OK to make an exception here or there. I remember what happened. I remember the deaths," he told reporters on Monday.
"I remember those terrible images and I will not ever allow that to happen again if it's within my power and where it's within my power."
He said smugglers remain active in Sri Lanka and Indonesia, and would act on any sign the government was weakening its position.
"That's not how you run strong borders.
"I know what happens when you send those messages back into those communities whether it's in Sri Lanka or the more than 10,000 people sitting in Indonesia right now who would get on a boat tomorrow if they thought this government was changing its position."
"I need to be very clear to those who might be sitting in Indonesia or Sri Lanka, or anywhere else, my government's policy has not changed."
The Prime Minister must personally intervene in this Biloela family case. It is sickening the Government is claiming they aren't legitimate refugees. Their two children were born in Australia!!! #Biloela #hometobilo— Alan Jones (@AlanJones) August 31, 2019
There were protests in capital cities across Australia at the weekend in support of Priya, her husband Nadesalingam and their Australian-born children Kopika, 4, and Tharunicaa, 2.
The family's deportation was halted last week, after it began, when a judge issued an injunction that saw their flight from Melbourne to Sri Lanka land in Darwin.
The family has since been transferred to Christmas Island, pending two court hearings that will decide their fate.
The Federal Circuit Court will on Monday afternoon consider if it even has the jurisdiction to hear the asylum matter.
The second hearing, scheduled for Wednesday, will examine the youngest child's case for Australia's protection.
The High Court has previously denied protection claims by the older child and the parents, who came to Australia separately by boat after Sri Lanka's civil war.
Earlier on Monday, Home Affairs Minister Peter Dutton said the family had been moved to Christmas Island to avoid potentially dangerous protests.
"I don't want a volatile situation in Victoria or in Darwin, where people are barricading this family in the hotel they were staying at," he told Nine's Today program on Monday.
But former deputy prime minister Barnaby Joyce says the family's case is special and deserves special treatment.
"The kids ... they are born in Australia. They are Australians as far as the community is concerned," he told Seven's Sunrise program.
"They are not their parents and I think we have to consider it in a different light. Time has moved on."
Lawyers for the family have complained the move to Christmas Island has severely impeded access to their clients.
Do you have a story tip? Email: email@example.com.