Thousands of people have rallied across the country demanding Priya, her husband Nadesalingam and their Australian-born children Kopika, 4, and Tharunicaa, 2, stay.

They are being held on Christmas Island after being granted an 11th-hour court injunction against their deportation.

"This is senseless cruelty, this is cruelty for the sake of being cruel," federal Greens leader Richard Di Natale told reporters at a rally in Melbourne on Sunday.

"This is a minister in Peter Dutton taking pleasure in the suffering of others, that's what going on here. It's barbaric, it's cruel and it needs to end."

Federal opposition leader Anthony Albanese pleaded for the government to make an exception and let the family return to their adopted community of Biloela, in regional Queensland.

"Minister Dutton has got himself in a circumstance whereby, in order to show that he's harsh and tough, he's showing that he has no humanity. Australia is a better country than that," he said.

Mr Dutton has refused to budge in the face of mounting community pressure.

"I would like the family to accept that they are not refugees, they're not owed protection by our country," he said on Friday.

The Tamil asylum seekers' case has been comprehensively assessed and reviewed since 2012, the Home Affairs department added.

It came as Federal Court Judge Mordy Bomberg extended an interim injunction against the deportation until Wednesday, after lawyers argued Tharunicaa had not been assessed for a protection visa.

The government had attempted to fly the family out of the country on Thursday night before the plane was ordered to land in Darwin because of the last-minute injunction.

But the family was flown to Christmas Island northwest of Australia the following night, and are believed to be the only people detained there.

"I spoke to Priya yesterday, she's very afraid," New Zealand journalist and family friend Rebekah Holt told Sunday's rally in Melbourne.

It was one of 15 planned across the country, including at Biloela.

"All I could hear in her voice was the stress, the exhaustion and the fear. I asked her if she had a message and she said 'we're all alone here'," Ms Holt said.

Hundreds of people gathered on the steps of the State Library of Victoria, chanting "Let them stay," before marching through the city.

In Sydney, crowds sang Twinkle, Twinkle Little Star for Kopika and Tharunicaa, while in Adelaide, people carried signs with slogans including "ashamed to be Australian".

The Tamil family's plight has also sparked support from unlikely corners, with radio shock jock Alan Jones speaking out in their favour.

Former Nationals leader Barnaby Joyce is also reportedly backing the family's bid to remain in Australia.

"The people of Biloela seem to be pretty enthused about keeping this family there. I think we should also be listening to them," he said, according to the Sydney Morning Herald.

Australian Associated Press