More than 30 babies born to asylum seeker mothers in Australia will be able to stay in the mainland with their families and not be processed on Nauru under a secret deal struck by crossbencher Ricky Muir.

Immigration Minister Scott Morrison announced the decision late on Thursday, immediately before a legal bid on behalf of the families failed in the Federal Court.

Senator Muir extracted the concession during tense negotiations with Mr Morrison earlier this month on sweeping changes to asylum seeker law, including the reintroduction of temporary protection visas.

He also secured an undertaking from Mr Morrison that the agreement would not only apply to 25 infants covered by the court challenge, but six others born on the mainland after their mothers were transferred from Nauru to give birth.

A jubilant Senator Muir welcomed the announcement, but expressed regret that the agreement would not apply to other children, possibly including one whose mother went into labour late on Thursday in the Royal Darwin Hospital.

"While this announcement is good news for these families, I still have concerns for the children and families that are currently on Nauru and the single men on Manus Island," Senator Muir, of the Motoring Enthusiast Party, said. "I intend to discuss these concerns with Mr Morrison early in the new year."

Mr Morrison said the decision was a "one-off" and had followed "representations made by Senator Ricky Muir".

It means those in the group who are found to be refugees will be granted a temporary protection visa or a safe-haven enterprise visa, which provides a potential pathway to permanent residency.

"Along with those 31 babies, I am also allowing their immediate family members to have their protection claims assessed in Australia," Mr Morrison said in a statement.

"This includes their mothers, fathers and siblings. That is around 80 family members, all of whom are already in Australia having been transferred from Nauru, for the birth of their child."

But Mr Morrison warned the almost 1000 asylum seekers on Nauru not to think his announcement "gives them a ticket to Australia".

They would remain on the island to be processed and would not be resettled in Australia, he said.

"The government's strong policies of turning back illegal boats, offshore processing and temporary protection visas remain in full effect," he said.

Until today, the children were considered both "unauthorised maritime arrivals" and "transitory persons", meaning none could be released or settled here.

The case, known as "Baby Ferouz", gained momentum after lawyers argued it was illogical to claim that babies who were born in Australian hospitals were classified as "unauthorised maritime arrivals".

Law firm Maurice Blackburn, representing baby Ferouz, said it welcomed the decision.

"Maurice Blackburn took this case on because of our belief that these babies were entitled to have their claims for refugee status considered, and that they should not be taken away, to languish in detention in Nauru," a spokeswoman said.

"Importantly, these babies and their families have only cleared the first hurdle – they still need to have their applications for refugee status considered.

"However, they at least now have that right and do not face imminent removal to Nauru."

But the decision does not extend to women who are pregnant, nor those who give birth after Thursday.

Mr Morrison's statement said: "Pregnant IMAs who were transferred to Australia but who had not given birth, prior to today, will also be returned to Nauru, with their babies, at an appropriate time."

The decision comes as every asylum seeker child on Christmas Island will be taken to Darwin by Christmas Day as part of a deal brokered with Senator Muir and other crossbenchers to get the controversial Migration Act through the Senate earlier this month.

With Adam Morton