The court has refused to hear an appeal on behalf of the youngest member of the Murugappan family, four-year-old Tharnicaa, who was born in Australia along with her older sister.

Their hopes of returning to their home in the small country town of Biloela in Queensland now sit with Immigration Minister Alex Hawke who must, under an earlier Federal Court ruling that went the family's way, consider whether Tharnicaa can apply for a protection visa.

Supporters hope that if Tharnicaa can win a visa her entire family will too, with the government previously saying it would not split them up.

Tharnicaa, her father Nades, mother Priya and older sister Kopika are living in Perth, after the latter three were granted three-month bridging visas in June.

They were finally released from years of detention - the last stint on Christmas Island - after Tharnicaa was medically evacuated from the island with a blood infection that left her gravely ill.

In a video message after Thursday's High Court rejection, Priya thanked Australians who have backed their fight against deportation to Sri Lanka, where she and her husband fear persecution.

The family is fearful about what will happen next month when their bridging visas expire, and desperately want to return to their community in Biloela but can't due to a government requirement that they stay in Perth.

Priya says her daughters are still under the care of doctors including for their mental health with most of their lives spent in detention.

"But this could happen back in my community of Biloela. Biloela is where the girls will get better and be safe," she said in the video message.

The High Court's refusal to hear Tharnicaa's appeal did not surprise supporters who say the court rarely allows applications. But they are not giving up.

"There are other options still on the table. There is still that tremendous amount of community support for the family. This isn't the end of the road at all," Home To Bilo campaigner Simone Cameron told AAP.

Lawyers for the family will head back to the Federal Court on September 16 to challenge the minister's decision not to let the family apply for another bridging visa when their existing ones expire.

Ms Cameron said another matter is before the Administrative Appeals Tribunal challenging the government's decision to register the girls' births in Sri Lanka, even though they were born in Australia.

"Priya and Nades at no point wanted Sri Lankan citizenship for their daughters. We think the government did that to make it easier to deport them," she said.

Ms Cameron is also nervous about what will happen when the family's bridging visas expire.

"The migration act stipulates that if you are not a citizen, and you don't have a valid visa, then you are an unlawful, non-citizen and anyone who is an unlawful non-citizen should be put in immigration detention," she said.

"They are at great risk of being put back into detention as of September 22 if the minister doesn't lift the bar in the meantime."

In a brief statement Mr Hawke noted the High Court decision but said it would be inappropriate to comment further given the ongoing legal matters.

Queensland Premier Annastacia Palaszczuk has again backed the family's fight to stay.

"They live in Biloela and I believe they should go home to Biloela," she said on Thursday.

Before they fled their homeland, Nades had links to Hindu Tamil Tigers insurgents, who battled Sri Lanka's majority Buddhist government during the country's civil war.

Australian Associated Press