The litigation guardian of Tharnicaa Murugappan had sought special leave to appeal to the nation’s highest court, but that was declined on Thursday.

Earlier this year the full bench of the Federal Court upheld a judge’s ruling that Tharnicaa had been denied procedural fairness when trying to apply for a protection visa to stay in Australia.

However, the court also upheld a judgement that Tharnicaa had not made a valid visa application back in 2019 and the family sought to challenge that in the High Court.

In June Immigration Minister Alex Hawke granted three-month bridging visas to Tharnicaa’s father Nades, mother Priya and older sister Kopika, who like Tharnicaa was born in Australia.

Hawke said at the time his decision allowed the three family members to live in Perth “while the youngest child’s medical care, and the family’s legal matters, are ongoing” and that Tharnicaa’s “visa status is unchanged”.

Before Tharnicaa was born her parents applied for protection visas but were unsuccessful, as were their court challenges on fairness grounds.

The family had been in detention for three years, being kept on Christmas Island from August 2019 when an urgent injunction stopped their deportation mid-flight.

They moved back to the mainland after Tharnicaa needed hospital treatment for a blood infection.

The family and their advocates say they remain hopeful despite the High Court decision, because the Federal Court judgment compelled Mr Hawke to review Tharnicaa’s eligibility for assessment as an asylum seeker.

“The matter is now in the hands of the immigration minister and he or she is able at any point in time to grant a visa including a visa that would allow the family to return to and live in Biloela where they would receive community support, stability, care and a sense of belonging,” the family’s lawyer Carina Ford said in a statement.

“The ethical, economic and compassionate decision to be made should be to allow them to stay and be returned home to Bilo.”

Priya Murugappan said both her daughters were still having medical treatment.

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

She and family friend Angela Fredericks appealed to the minister to let the family return to Biloela.

“It is really sad that we have a four-year-old needing to go to court against the Australian government, just to get them to look at the risk of being sent to a dangerous country she has never been to,” Fredericks said.

But in a brief statement Hawke said as the family had a number of other ongoing legal matters, it was inappropriate to comment beyond noting the High Court decision.