Mr Dutton has rounded on the couple, saying the reason they've been in Australia for so long is because they have refused to accept rulings that they are not genuine refugees.

He said "excessive" appeals had kept them here and now they were complaining about having to leave the life they established in the Queensland town of Biloela.

"People have the ability to appeal. That's their legal right," Mr Dutton told reporters on Tuesday.

"But you can't appeal, refuse the umpire's decision and then delay and delay and delay through subsequent appeal processes and then say it is unfair that you have been here so long and therefore you have established those connections to the community.

"It doesn't cut both ways."

He said Priya and Nadesalingam's Australian-born children Kopika, 4, and Tharunicaa, 2, had been put in an unfair situation.

"I think it is unfair to the children in this case where the parents were given a very definite decision that they weren't going to stay here in Australia many years ago and the kids have been drawn through - or dragged through - that process in the subsequent years."

The family remains detained on Christmas Island before a court hearing on Wednesday to test the youngest child's case for Australia's protection.

A succession of courts, including the High Court, have found the parents and the oldest child are not refugees and do not qualify for Australia's protection.

Mr Dutton would not say how quickly the family would be deported to Sri Lanka, if they lost the court battle.

The home affairs minister has also come out swinging against Labor after senior opposition figures suggested the prime minister's refusal to intervene in the case was incompatible with his Christian beliefs.

Labor frontbencher Joel Fitzgibbon has said the Morrison government's stance is "not particularly Christian".

And home affairs spokeswoman Kristina Keneally said Scott Morrison should explain his position through the lens of his religious beliefs.

"I'm calling on him to reflect upon the parable of the Good Samaritan, which invited us as Christians to take care of the stranger in our land," the Catholic Labor senator told the ABC on Tuesday.

The government has warned of a return to the dark days of mass drownings at sea if it makes an exception for a family deemed ineligible of protection.

They say people smugglers will kick their trade back into high gear if there's a perception Australia is showing leniency towards illegal boat arrivals like Priya and Nades.

Nades has said his links to Tamil Tigers insurgents who battled Sri Lanka's government during the country's civil war mean he's in danger of persecution if he goes home.

But Mr Dutton says he travelled back to Sri Lanka on a number of occasions and he had been unable to convince a succession of courts that he would be in danger.

Nades and Priya came separately to Australia illegally by boat after the war ended. They met here and had two children before settling in Biloela.

The town has waged a spirited campaign to get the family back since they were put in immigration detention last year.

Since then the family's plight has gained national attention, with a series of supporting rallies staged in capital cities on the weekend.

Australian Associated Press