A spokesperson from the Department of Home Affairs said in a statement it was considering the implications of the court's decision.
"The Australian Government's policy is clear — no-one who attempts illegal maritime travel to Australia will be settled here," the spokesperson said.
"The family's claims to engage Australia's protection obligations have been comprehensively assessed on a number of occasions by the Department of Home Affairs, various merits review bodies, and appealed though multiple courts, including the Federal Court to the High Court.
"At no time has any member of the family been found to be owed protection."
The spokesperson said "non-citizens who do not hold a visa and who have exhausted all outstanding avenues to remain in Australian are encouraged to depart voluntarily".
"Those unwilling to depart voluntarily will be subject to detention and removal from Australia, as has occurred in this case," the spokesperson said.
