The federal government is pushing ahead with its challenge to the federal court’s ability to order sick refugees and asylum seekers be brought to Australia, despite signalling its willingness to remove all children from Nauru within weeks.

On Thursday it was revealed the government had given itself to the end of the year to bring the remaining 38 children and their families on Nauru to Australia.

But on Friday, lawyers representing the Department of Home Affairs will appear before a full bench of the federal court to argue that the court does not have the jurisdiction to hear cases involving transfers, relying on a subsection of the Migration Act which prevents Australian courts – other than the high court – hearing cases on “transitory persons”.

The home affairs minister, Peter Dutton, told Sky the deadline had nothing to do with medical concerns, instead saying the operation of the two centres on Nauru and Manus Island were costing taxpayers about $1bn a year. His comments were at odds with the messaging from the prime minister, Scott Morrison, who has said the government was “quietly” getting on with bringing children to Australia for medical care.

The vast majority of recent medical transfers have involved either a federal court order forcing Australian Border Force to bring the patient and their family to Australia, or have occurred under concession after legal action was commenced.

Just 49 of 135 people transferred since 15 October have been brought to Australia under the initiative of ABF.

The challenge is part of a case involving an 11-year-old Iranian child who has since been evacuated to Australia.

If the government is successful it would likely force all future cases to go to the high court, and could void previous orders under which more than 90 people were transferred to Australia. Another 240 were transferred after legal proceedings were launched or threatened.

The Human Rights Law Centre and private firm Robinson Gill lawyers are representing the girl.

“This has come out of the blue,” said the centre’s director of legal advocacy, Daniel Webb.

“The government has never raised this argument in any of our previous cases, and there’s a real risk it could make it much harder for desperately unwell people to get the urgent, lifesaving medical care they need.”

Since 15 October, 47 children have arrived in Australia from Nauru. They have been sent to cities around the country which have the appropriate health services. At least 10 children have been admitted to hospital.

The director of the National Justice Project, George Newhouse, on Thursday queried why the government was pushing ahead with its challenge while conceding that people needed to be brought off the island.

“We’ve still got the men on Nauru and Manus, and the women on Nauru that still need help,” he told Guardian Australia. “Once you get the kids off they’re going to need help. [The government] might be shutting down an avenue for remedy.”

There are more than 600 people still on Nauru, including more than 500 refugees.

The government has also signalled it intends to keep control of the Nauru processing system by renewing its contract with the garrison and welfare services provider Canstruct for another six months.

Nauru had intended to take over the running of the centre from Australia, but the handover continues to be delayed, with island sources saying it is not yet prepared.

Last week the Home Affairs department revealed it was seeking to extend the Canstruct contract for at least six months. Guardian Australia has confirmed the contract with the Brisbane-based company has been extended, with the permission of the Nauruan government.

The previous 13-month contract, which expired at the end of last month, was for $377m.

The Nauruan government legislated to establish the Nauruan Regional Processing Centre Corporation to manage the centre. Currently garrison services and other providers are still contracted by the Australian government, but they must be approved by the RPC Corp.

The Nauruan government did not respond to requests for comment.