Home Affairs Minister Peter Dutton has referred to the children in a Tamil asylum-seeker family facing deportation as “anchor babies”.

Mr Dutton said the family’s long-running fight for Australian protection had cost taxpayers “literally millions of dollars”.

“It’s been made very clear to them at every turn that they were not going to stay in Australia and they still had children,” Mr Dutton told 2GB radio on Thursday.

“We see that overseas in other countries – anchor babies, so-called – and the emotion of trying to leverage a migration outcome based on the children.”

The Sri Lankan couple came separately to Australia by boat several years ago before marrying, having two children and settling in the central Queensland town of Biloela.

They are now in detention on Christmas Island as the Federal Court decides whether the youngest child is eligible for protection in Australia.

Labor’s home affairs spokeswoman Kristina Keneally first raised the prospect of debate around the family straying into “anchor baby” territory during an ABC radio interview last week.

Peter Dutton is resolute in his determination the family will not be settling in Australia.

“This is an importation, quite frankly, of an American debate about so-called ‘anchor babies’ and the law is very different in the United States where citizenship is accorded to anybody born on American soil,” she said.

“That is not the law in Australia so it’s an importation of that debate.”

Senator Keneally said the real issue at hand was that Biloela locals and Australians more broadly had embraced the family and wanted to integrate them into the community.

“It’s not simply the act of having a child,” she said.

Mr Dutton said the latest legal challenge would take some time to resolve.

“I think it will go on now for potentially a couple of months because lawyers will try and delay and that’s part of the tactic,” he said.

“They think that if they delay they can keep the pressure up on the government and we’ll change our mind in relation to this case.”

Family friend and Biloela resident Angela Fredericks said she spoke to several MPs in Canberra on Wednesday about the family’s plight.

“What I realised was that many politicians remain unaware of the facts of this case,” she said on Thursday.

The family’s case has been through a number of courts, who found that it was within the power of bureaucrats to reject their asylum claims.

They will remain in detention at least until September 18, when the case is due back in the Federal Court in Melbourne

-AAP