The future of Australia's offshore detention regime has come under the spotlight in the High Court of Australia in Canberra.

Lawyers for a Bangladeshi woman argued it was illegal for the Australian Government to operate and pay for offshore detention in a third country.

If the court agrees, the whole offshore detention regime could be invalid.

Nauru announced on Monday it would end detention and process refugee applications for the remaining 600 asylum seekers by the end of the week.

But the Australian and Nauruan governments deny the move had anything to do with the imminent High Court hearing.

Human Rights Law Centre's director of legal advocacy Daniel Webb said the changes to the detention arrangements on Nauru were "one of the issues before the court".

"Irrespective of these changes, there remain important and untested constitutional questions about the power of the Australian Government to pay and to control the detention of innocent people in other countries," he said.

"Allowing people the freedom to go for a walk does not address the fundamental injustice inherent in leaving them languishing indefinitely on a tiny pacific island."

Mr Webb said the case was being run on behalf of the Bangladeshi woman who was brought to Australia due to a serious deterioration in her health during the late stages of pregnancy and "who was now facing imminent return to Nauru with her 10-month-old baby".

Recent challenges to offshore processing in High Court: August 31, 2011 - The High Court threw out the Labor government's "Malaysia solution" ending a plan to send asylum seekers there for processing. The court found Malaysia could not be designated as a regional processing country because it was not legally bound by international or local laws to protect refugees. June 18, 2014 - Australia's offshore processing operation in Papua New Guinea was upheld by the High Court. The court found in this case the law designating PNG as a regional processing country was valid under the aliens power in section 51 of the constitution. October 7, 2015 - The High Court will rule again on the validity of offshore processing. This time the question is whether the constitution allows the Government to remove people to a third country to be held in detention.

"This is the lead case linked to a series of challenges being run on behalf of more than 200 people in similar situations who have been brought to Australia from Nauru and Manus," he said.

"They include men subjected to serious violence on Manus, women who've been sexually assaulted on Nauru and over 50 children, including 23 babies."

The High Court heard the argument that the woman's return and continued detention at Nauru would be illegal because Australian laws set up to support the offshore program were unconstitutional.

The case centres around whether the Government has the power to spend on large programs without parliamentary approval.

In June the Government passed changes to the Migration Act with the support of the Opposition to close a loophole it feared would see the High Court declare the entire system illegal.

The issue of parliamentary approval for funds for major policies was brought to light by the earlier school chaplains case where the High Court ruled large sums could not be allocated to programs without parliamentary approval.

The Government had to make new laws to ensure funding for a raft of its programs.

Lawyers for the woman said they had challenged the new law as part of their case.

The court heard there was no constitutional power supporting the arrangement where the Government can send people offshore to be detained in a third country.

But the Government said the law was supported by several parts of the constitution, including the aliens power and the external affairs power.

Nauru announcement means challenge would be pointless: Commonwealth

On Wednesday, lawyers for the Commonwealth asked the High Court to throw out the challenge, saying the recent announcement by the Nauruan Government would give asylum seekers at the site more freedom.

They argued this meant there was nothing left in the case.

"Our primary submission is there's now nothing left in this case where the court could give relief in respect to the future because of those facts," Solicitor General Justin Gleeson said.

"The question has fallen away.

"Knowing that the facts now are radically different we would submit the court would not even entertain an injunction or prohibition."

Solicitor General Gleeson said for the court to make a ruling on whether the Commonwealth lacked authority in this matter had "no relevant foreseeable consequence for the plaintiff".

The hearing will continue on Thursday.

The Human Rights Law Centre said it had commenced legal action for more than 200 people who have been brought to Australia for medical treatment but were now facing forcible removal to Nauru.

While the legal issues are being contested, the Federal Government has promised not to return any of them without notice.