The legality of Australia's role in the Nauru immigration detention centre is being examined by Australia's High Court.
The hearing before the full bench today comes two days after the Nauru government made the centre an open facility and vowed to finalise all 600 outstanding refugee claims this week.
The test case focuses on the plight of a pregnant Bangladeshi asylum seeker brought to Australia from Nauru because of serious health complications.
She is now facing imminent return to the Pacific island with her 10-month-old baby.
The Melbourne-based Human Rights Law Centre is also running more than 200 other cases on similar legal principles.
"Australia should not be indefinitely warehousing people on remote islands, especially babies," said spokesman Daniel Webb.
The family was terrified of being forced back to an unsafe environment, he said.
The plaintiff's lawyers will argue there is no law that gives the federal government power to fund offshore detention centre arrangements.
The government responded by hastily passing retrospective legislation, Mr Webb said.
The High Court's ruling could also have legal implications for the other offshore detention centre on Manus Island, Papua New Guinea.
Lawyers for the Commonwealth say the plaintiff's case could not form the basis of a damages claim because that would fall under Nauruan law.
They will also argue that it is clearly within the non-statutory executive power of the Commonwealth to enter into a memorandum of understanding with the Nauru government.
Australia's immigration minister said Nauru's announcement that it would process all remaining asylum seekers within the next week was unrelated to the court case.
"It's not just an announcement 48 hours... before a court case," Peter Dutton told the ABC on Tuesday.
"There are High Court cases, court cases, going on all the time between advocates and the Federal Government, between advocates and other parties, and these matters continue to roll through the courts."
"The start of detention-free processing is a landmark day for Nauru and represents an even more compassionate programme, which was always the intention of our government," Nauru Justice Minister David Adeang said in a statement.
Australia would provide more police assistance to help Nauru with "safety, security and law enforcement", Mr Adeang said.
Successive Australian governments have vowed to stop asylum seekers reaching the mainland, turning boats back to Indonesia when it can and sending those it cannot for detention in camps on Manus island in impoverished Papua New Guinea and on Nauru.
The harsh conditions at the camps, including reports of systemic child abuse, have been strongly criticised by the United Nations and human rights groups. An independent UN investigator postponed an official visit to Australia last month, citing a lack of government cooperation and "unacceptable" legal restrictions.
New Australia Prime Minister Malcolm Turnbull said last month he was concerned about conditions in the camps but gave no indication of a major policy change, so Monday's announcement from Nauru came as a surprise.
- AAP / ABC / Reuters