His government also revealed boats have been coming from Sri Lanka for months, only to be turned around by Australia's border patrols.

The man with a trophy in his office celebrating how he stopped the boats says granting an exception for a family whose asylum claims had been denied would kick-start the people smuggling trade.

The prime minister said the government could not 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," Mr Morrison 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 people smugglers remain active in Sri Lanka and Indonesia, and would act on any sign the government was weakening its position.

"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," he said.

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 a judge issued a last-minute injunction that saw their flight from Melbourne to Sri Lanka land in Darwin.

The family has since been transferred to Christmas Island, pending a Wednesday court hearing to decide their fate.

An action in the Federal Circuit Court on Monday afternoon was shifted to combine with Wednesday's Federal Court hearing, which 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 and illegally by boat in 2012 and 2013 after Sri Lanka's civil war.

The government says they have had their asylum claims assessed several times and found not to be genuine refugees.

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.

"The kids ... they are born in Australia. They are Australians as far as the community is concerned," he told the Seven Network.

"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.

Australian Associated Press