The mother from the Tamil family at the centre of an immigration row has spoken of her family's ordeal at a Christmas Island facility, as hundreds of people rallied around the country to urge the Government to let them stay in Australia.

Key points: Priya said Border Force officials initially took the family's phones and there was "no freedom" within the centre

Priya said Border Force officials initially took the family's phones and there was "no freedom" within the centre Rallies were held across the country in support of the family, including a moment of silence in Biloela

Rallies were held across the country in support of the family, including a moment of silence in Biloela The Department of Home Affairs has found the family are not genuine refugees

Priya said she, her husband and their two daughters had been holding out hope of a return to their Central Queensland home of Biloela since a last-minute court injunction stopped their deportation on Thursday night.

But she said her daughters were crying "all the time" and had not been eating properly since they were move from the Melbourne immigration centre.

Priya and Nadesalingam, also known as Nades, came to Australia separately by boat in 2012 and 2013 and their daughters Kopika, 4, and Tharunicaa, 2, were born in Australia.

The Department of Home Affairs said the family had been comprehensively assessed a number of times and had consistently been found not to be genuine refugees.

Children made signs in support of the family in their former home of Biloela. ( ABC News: Erin Semmler )

Following the injunction, the Federal Court ruled on Friday that Tharunicaa should not be deported from Australia until 4:00pm Wednesday.

The family was moved from Darwin to a Christmas Island detention centre in the early hours of Saturday morning, lawyers said.

In the small town of Biloela, more than 50 people gathered to tell the Government they want the Tamil family back with them.

A moment of silence was observed for the family and tears were shed as demonstrators sung songs.

'No freedom' in empty Christmas Island facility, mother says

Priya said Border Force officials initially took the family's phones and there was "no freedom" within the centre.

"The children are tired, very upset. It's a very hard time," she told the ABC on Sunday morning.

Speaking on the phone from Christmas Island, she said the family were alone and the building was "very old" and dusty.

She said the girls were "crying all the time," pleading to leave and had not been eating.

Family friend Vashini Jayakumar said the ordeal had "terrified" Priya as a mother.

"They just feel terrible. I don't know how to express that. It's just a very hard time for them," she said.

Priya said she sustained injuries during Thursday night's deportation that were being treated on Christmas Island but were "very painful".

Advocates for the family said the mother had a blood pressure condition and had not received medication to treat it.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 2 minutes 8 seconds 2 m 8 s Through family friend Vashini Jayakumar, Priya told the ABC her daughters were "very upset".

The Department of Home Affairs did not comment on the condition of the family or confirm their location, saying it would be inappropriate as the matter is before the courts.

"Unlawful non-citizens are only removed if the Department is satisfied they do not engage Australia's non-refoulement obligations and that removal would not breach Australia's international obligation," a spokesman said.

Supporters push for ministerial intervention

Lawyers will fight the deportation in the courts, but a campaign to keep the family in Australia has urged Home Affairs Minister Peter Dutton to intervene in the case.

About 200 supporters took their message to Parliament House in Canberra. ( ABC News: Tahlia Roy )

Former deputy prime minister and Nationals leader Barnaby Joyce joined the chorus of voices asking for the family to stay on Saturday.

He told Nine newspapers "I think we should be listening" to the people of Biloela, who want the family to stay.

But he said he was "certainly not here to tell the Minister how to do his job".

Priya said her daughters Tharunicaa (left) and Kopika (right) had not been eating. ( Supplied: Tamil Refugee Council )

Opposition Leader Anthony Albanese, who usually has a bipartisan approach to border protection, said he had raised the issue with the Prime Minister and suggested Mr Dutton needed to intervene in the case.

"The fact that the family were moved from Darwin to Christmas Island to get them out of public view is, I think, just quite extraordinary," he said.

"What was the cost of that move for the Australian taxpayer?"

Greens Leader Richard Di Natale said the treatment of the family was "senseless cruelty".

"It is barbaric, it is cruel and it needs to end," he said.

Mr Dutton said on Friday the family had been found "all the way to the High Court" not to be owed protection.