A judge has extended the injunction preventing the deportation of the Biloela Tamil family until 4pm Thursday, saying he needs more time to consider his decision.
Justice Mordy Bromberg made the ruling on Wednesday afternoon as the hearing into the family's two-year-old daughter's right to apply for a protection visa continued.
Parents Priya and Nades Murugappan and their daughters Tharunicaa, two, and Kopika, four, are being held in detention on Christmas Island awaiting the court's ruling.
The federal government's plans to return the family to Sri Lanka were put on hold by a previous injunction which expired at 4pm Wednesday, with Justice Mordy Bromberg making orders which stretch the deadline until 4pm Thursday.
Justice Bromberg is expected to deliver his decision on Thursday at 2.15pm on whether the matter proceeds to a "full and final" hearing and whether the family remains in Australia until that time.
Earlier, lawyers for the family told the Federal Court that two-year-old Tharunicaa Murugappan was legally entitled to make a visa application when "the bar was lifted" between July and August 2017, following a determination by Home Affairs Minister Peter Dutton.
That change lifted the usual limitation to apply for a visa under the Migration Act, which ordinarily deems that children of asylum seekers who arrive by boat are not entitled to refugee status.
A protection visa was made for Tharunicaa last week, with barrister Angel Aleksov arguing that bar should remain lifted to assess her right to stay in Australia.
"It is a very serious question about whether my client has been lawfully detained," he said.
But Stephen Lloyd, acting for the federal government, said the bar was only lifted temporarily and that no application was made during that time.
Mr Aleksov argued the minister should be required, and in fact had a duty, to consider Tharunicaa's claim, with the only issue being whether she was "disqualified" under immigration legislation.
"This all turns on whether there was a power to remove ... because there was a statutory process still in place".
Mr Aleksov also argued if the family was deported, it was a situation of "literally life or death", but conceded there was no evidence before the court about the risk of serious harm in Sri Lanka.
The family had settled in the Queensland township of Biloela before being taken into detention, with Tharunicaa's parents and sister already refused refugee status in Australia.
Tamil Refugee Council spokesman Aran Mylvaganam said he had spoken to Priya and Nades from Christmas Island overnight, when they relayed their jail-like conditions, surrounded by guards.
"The circle of guards have been ordered by Australian Border Force to capture every moment of their stay there on video," he told AAP on Wednesday.
On 7 September, Justice Bromberg extended an injunction until 4pm on Wednesday, preventing the government from deporting the family, which also includes four-year-old sister Kopika.
But with lawyers continuing to argue for an injunction through the Federal Court, the family is unlikely to be deported before a "full and final" hearing at a later date, still to be scheduled.
The interlocutory hearing in Melbourne continues.
