SYDNEY (DPA) - A Tamil family with two young children born in Australia was granted a further 12-day reprieve from deportation to Sri Lanka by a Melbourne court on Friday (Sept 6).

The court ordered the government to provide more evidence to support its argument that the youngest child, an Australian-born two-year-old, has no claim for protection before the family could be deported.

Unlike the rest of the family, the two-year-old had not yet been assessed for a protection visa. It is not clear what will happen to the rest of the family if the court rules in the toddler's favour.

Federal Court Justice Mordecai Bromberg will hear a "full and final" hearing for the case on Sept 18, the national broadcaster ABC reported from the court.

Priya, Nadesalingam and their two children Kopika, four, and Tharunicaa, two, are being held on remote Christmas Island after a last-minute court injunction prevented the government from deporting them last week.

Migration officials had bundled the family onto a late-night plane bound for Sri Lanka, but a judge's midnight injunction forced them to be offloaded in Darwin pending court hearings.

The family's case has prompted emotional calls across the country, including from both sides of politics, for them to be allowed to stay in Australia.

The couple arrived separately by boat from Sri Lanka in 2012 and 2013. They had applied for asylum in Australia, but a succession of courts found they did not qualify as refugees.

The government argues that if they were allowed to stay it would lead to a flood of asylum seekers trying to reach Australia by boat.