The Tamil family fighting deportation to Sri Lanka will remain in Australia for at least 12 more days after a Federal Court judge ordered the Immigration Minister to provide more evidence to support claims the youngest child has no right to protection.

Key points: The court ruling allows the family to remain in Australia until at least September 18

The court ruling allows the family to remain in Australia until at least September 18 A date for a full hearing of the case could be set at that point

A date for a full hearing of the case could be set at that point The family's lawyer said she expected the order preventing their deportation would be extended until a final decision was made

The case will return to court for an interlocutory hearing before Federal Court Justice Mordecai Bromberg on September 18.

Justice Bromberg ruled the family — Nadesalingam Murugappan, known as Nades, and Kokilapathmapriya Nadesalingam, known as Priya, and their two children — cannot be deported before that hearing.

But the judge said the September 18 date would not be a "full and final" hearing of the case as that would require significant preparation.

The couple and their children, four-year-old Kopika and two-year-old Tharnicaa, had been on remote Christmas Island since last Friday, after their lawyers obtained an injunction to prevent their deportation based on claims the youngest child's claim needed to be independently assessed.

Last Thursday the family was taken from immigration detention in Melbourne and put on a charter plane bound for Sri Lanka.

Supporters of the family gathered outside the Federal Court building before today's hearing. ( ABC News: Elias Clure )

The plane was forced to land in Darwin after the family's lawyer obtained a late-night injunction to prevent their deportation.

The injunction only applied to two-year-old Tharnicaa, but the family's lawyers have said they were given assurances the family would not be split up.

On Wednesday the court was told she had been assessed and that Immigration Minister David Coleman would not exercise his discretion to allow her to apply for a protection visa.

Lawyers for the family have questioned the assessment process, which happened quickly and on the same day citizenship was sought for the toddler.

Lawyers urge ministerial intervention in 'exceptional case'

The court action has 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.

The family's asylum claims had been repeatedly rejected. ( Supplied: Tamil Refugee Council )

Former deputy prime minister Barnaby Joyce is among several politicians to express support for the family, placing him at odds with some of his Coalition colleagues.

Home Affairs Minister Peter Dutton and Prime Minister Scott Morrison have repeatedly said the Government would not intervene in the family's case.

Outside court, lawyer Carina Ford said she remained hopeful the Government would use ministerial discretion to keep the family in Australia.

"We're just saying this is an exceptional case," she said.

She said there would be "a lot of filing of documents" between now September 18 and and that a full hearing date could be set at that point.

Ms Ford said she expected the injunction preventing the family's deportation would be extended until a final decision was made.

Mr Dutton, who oversees the immigration portfolio handled by Mr Coleman, has said on many occasions the family has been found to have no right to protection in Australia.

Their case has been taken all the way to the High Court.

Lawyers have acknowledged that they have an uphill battle even if they are successful in their current litigation, as the determination of refugee status will go back to a department delegate who will determine if the Minister should consider intervening.

"That's the battle that we have, we need a change of heart ultimately," Ms Ford told the ABC on Monday.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 42 seconds 42 s Speaking before the case was heard in court, Peter Dutton ruled out fast-tracking visas for the family.

Children 'really upset' on Christmas Island, supporter says

The family say as Tamils they will be persecuted if they are forced to return to Sri Lanka.

Ms Ford said "there's no doubt it's stressful" for the family on Christmas Island.

"Litigation is stressful for anyone who's gone through it, but it's even more stressful when you're detained in an area you don't know and in the circumstances that they are," she said.

The family's lawyers amended the claim to include Mr Dutton and the secretary of the Department of Home Affairs Mike Pezzullo as respondents.

Ms Ford said that was "mostly procedural rather than anything political".

Family friend Angela Fredericks from Biloela visited the family in the Christmas Island detention centre.

"I've had three visits with them while I was here," she said.

"Today I got to visit them after the court announcement had been made. The family reported that they were feeling very relieved and happy today.

"They are of course very concerned about what's going to happen, they know that it's far from over, however I guess they are very hopeful that they are still here, that there's still hope."

Ms Fredericks said they were continually guarded by anywhere from six to eight guards at a time.

"The guards check on them throughout the night, every two to three hours. They are in a very small bedroom. There is one set of bunk beds.

"So basically, Nades and Kopiga sleep on the top bunk and Priya and Tharunicaa sleep on the bottom bunk.

"They've said that they've got some nice guards looking after them, they do have access to a doctor.

"They are lonely. There are no other detainees there so it is quite lonely, there's only the guards."

Family friend Bronwyn Dendle said the extension gave supporters more time to rally behind the family.

"I was worried if it didn't go their way this afternoon they would be sent back so we are relieved we've got more time now for the public to continue to show their support and petition their members to let them go home to Bilo," she said.

She said she expected Priya and Nades would be relieved for the time being, but would be struggling over the next week on Christmas Island.

"It's no place for two little kids, so it is disappointing they're so far away from their supporters.

Ms Dendle said Priya had called her last night.

"She's feeling anxious, she's feeling worried and the kids are feeling really upset, but she wanted to ring me to make sure I let everyone know how much she appreciates their support."