A Tamil family facing deportation has been given until Friday to consider a "surprise" development in their case, after the Immigration Minister said he would not exercise his discretion to allow the youngest daughter to stay in Australia.

Key points: The family's lawyer said the Government had told them to abandon the case because it was "futile"

The family's lawyer said the Government had told them to abandon the case because it was "futile" An affidavit from the Immigration Minister said two-year-old Tharunicaa's case had been assessed

An affidavit from the Immigration Minister said two-year-old Tharunicaa's case had been assessed But the family's lawyer said it was the first they had heard of a departmental assessment

The Federal Court heard the Immigration Minister David Coleman had advised the family's lawyers that the department would not allow two-year-old Tharunicaa to apply to renew her visa and that her case had been assessed.

Justice Mordecai Bromberg extended the injunction preventing the family's removal from Australia until 4:00pm on Friday.

The family had been advised by the Government to abandon the case preventing the transfer "because it is futile", their lawyer Angel Aleksov said.

The case has been set down for a further hearing on Friday.

Nadesalingam Murugappan, known as Nades, and Kokilapathmapriya Nadesalingam, known as Priya, arrived in Australia from Sri Lanka separately by boat in 2012 and 2013.

Supporters for the family gathered outside the court in Melbourne. ( ABC News: Gemma Hall )

Their young daughters — four-year-old Kopika and two-year-old Tharunicaa — were born in Australia.

Nades and Priya's applications for asylum have been turned down repeatedly.

On Thursday last week, lawyers representing Tharunicaa were able to get a last-minute injunction to stop the removal of the family from the country.

A Border Force plane en route to Sri Lanka was forced to land in Darwin in the early hours of Friday morning to comply with the order.

The injunction applied only to the two-year-old, but the family had been kept together as the matter was assessed.

Toddler's application already assessed, court hears

In a hearing last week, Mr Aleksov told the court Tharunicaa had not been assessed by immigration officials as to whether she was entitled to protection, but should have been.

On Wednesday, the court heard an affidavit filed overnight said "the Minister has decided not to consider exercising his discretionary power … to permit the applicant [Tharunicaa] to make an application for a protection visa".

The two children were born in Australia. ( Supplied: Tamil Refugee Council )

The court heard the toddler's original visa had expired "at the end of the judicial review process".

The court heard her case had been assessed by someone in the Department of Home Affairs.

Mr Aleksov, acting for the family, said the affidavit was "the first we've heard about that".

Justice Bromberg asked Mr Aleksov if he would be able to proceed on Friday "without any further surprises".

Outside court, another of the family's lawyers, Carina Ford, said the family was in "uncertain territory".

"But I guess the fight is not over yet," she said.

Ms Ford said the lawyers had not been allowed a response to the issues raised in Mr Coleman's affidavit and would be requesting the documents detailing any assessment of Tharunicaa's asylum claim.

She said the family, who were flown to Christmas Island late Friday night, remained "relatively distressed" but understood the court process as best they could.

Case 'traumatic' for Biloela community

The events of the past week have been closely watched by the family's supporters in the central Queensland town of Biloela, where the family lived for four years until early 2018 when they were placed into immigration detention.

People in Biloela rallied in support of the family on Sunday. ( ABC News: Erin Semmler )

Family friend Jayne Centurion said the long and drawn-out process had been "traumatic" for the community, and no doubt the family.

"It breaks our hearts that we're still waiting, with no outcome at all. We love these people … they're beautiful souls."

Supporter Marion Meisner said she was hopeful the delay would bring a positive outcome.

"But [I'm] very concerned that there's still not a resolution for lovely people who are just trying to get on with their lives," she said.

Speaking in Melbourne ahead of the court decision, Prime Minister Scott Morrison said the case was a matter of national security.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 1 minute 38 seconds 1 m 38 s Biloela resident Laraine Webster called for the return of the family to the town.

"It's about doing the right thing by the national interest. It's not about chasing public sentiment," he said.

"And I understand, absolutely, the motivation and the compassion that Australians have expressed in relation to this case. I understand that. And I understand it's what motivates the suggestions that they're making.

"But I also know from bitter experience, that if you make the wrong calls on these issues then you invite tragedy and you invite chaos."

Opposition Leader Anthony Albanese travelled to Biloela shortly after the court decision, where he urged Mr Morrison and Home Affairs Minister Peter Dutton to visit the town themselves.

"It's not too late for the Government to recognise that this isn't a threat to its immigration policy. It's not a threat to Australia's borders," he said.

Mr Albanese said he was not calling for a policy change, but for the Government to intervene.

He pointed to Mr Dutton's intervention to prevent two au pairs on short-term visas being deported — as an example of ministerial discretion being used in immigration matters.