The family of four including two young children, who previously lived in the rural Queensland town of Biloela, have been detained on Christmas Island as they fight the deportation.

Mother Priya Murugappan was flown to Perth at the weekend after suffering severe abdominal pain.

The home affairs minister bemoaned the fact the federal government provided the charter flight and claimed her tests revealed no medical issues.

"I wish her every good health and a speedy return back to Sri Lanka," Mr Dutton told 2GB radio on Thursday.

"But this is a situation that is of their own making - it is ridiculous, it is unfair on their children - and it sends a very bad message to other people who think they can rort the system as well."

Mr Dutton said the family was "playing funny games" through the courts to prevent their detention and costing taxpayers a fortune in the process, pegging the cost at more than $10 million.

"These people have been found all the way to the High Court not to have a claim for protection," the minister said.

"They are not refugees and they have used every trick in the book to make sure they can stay."

The family has been locked in a marathon legal battle with the Australian government and is awaiting another court date.

A Federal Court judge ruled in April their deportation must remain on hold after determining the youngest daughter, who was born in Australia, was denied procedural fairness in her bid to apply for protection.

"I want it to come to an end," Mr Dutton said.

"I want them to get on with their lives back in Sri Lanka, and we are determined to make sure that is the case."

Australian Associated Press