Labor Leader Anthony Albanese says Peter Dutton hasn't intervened to save a Tamil family from deportation because they are not as well connected as the family of two au pairs the Home Affairs Minister released from immigration detention.

Mr Dutton is continuing to resist growing pressure to allow the family whose two young children were born in Australia to stay and intends to deport them to Sri Lanka once an injunction lifts on Wednesday.

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Mr Albanese told 2GB's Alan Jones on Tuesday morning that his response was very different when he was asked to help two au pairs who had been wrongly granted tourist visas.

"The only difference here is that in the au pair cases someone had Peter Dutton's mobile number to ring him," Mr Albanese said. "That's the difference here."

He said Section 195A of the Migration Act allowed for ministerial intervention and the issuing of any visa deemed appropriate to an individual's circumstances.

Mr Dutton has exercised this power more than 4,000 times to grant somebody a visa to live in Australia since taking on the immigration portfolio.

In the case of the two au pairs, Mr Dutton intervened to reverse decisions taken by immigration officers to cancel the women's tourist visas because they believed they were intending to work.

One was an Italian au pair employed by Mr Dutton's former Queensland police colleague and the other was a French au pair employed by relatives of AFL boss Gillon McLachlan.

Mr Albanese, who spoke to Scott Morrison on the weekend, told 2GB, it didn't matter that the Tamil family, who had settled in the Queensland town of Biloela, had had their refugee claims rejected.

"Literally millions of Australians have come as economic migrants here or are descendants of people who have come in that fashion."

But Mr Dutton has no intention of changing his mind.

"We are one of the most compassionate countries in the world in terms of the numbers we accept, but we have to have an orderly migration program," Mr Dutton told Seven's Sunrise on Tuesday morning.

The government argues that granting an exception to the family because of the strong public reaction would encourage people smugglers to continue their trade and risk lives.

The family was transferred to Christmas Island and a court hearing on Wednesday will decide their fate.