Addressing the case, Home Affairs Minister Peter Dutton said it was time for them to go home, Xinhua news agency reported.
"I would like the family to accept that they are not refugees, they're not owed protection by our country," he told the media.
The Australian Border Force (ABF) on Thursday night attempted to deport asylum seekers Priya, her husband Nadesalingam and their two Australian-born daughters.
The couple came to Australia by boat separately six years ago.
A last minute injunction from the Federal Court forced the plane transporting the family from Melbourne back to Sri Lanka to land in Darwin.
"They came here by boat and we've been very clear that they couldn't stay. We have brought in many families but in this case they have been found to the High Court not to be refugees," said Dutton. "We will help them resettle in Sri Lanka."
Representing the family in court on Friday, lawyer Angel Aleksov argued that the couple's daughters were owed protection by Australia because they were born in the country.
The family will now make an application for a visa in the name of two-year-old Tharunicca.
Christopher Tran who represented the immigration department and David Coleman, the Minister for Immigration, said in court that the family's removal from Australia was inevitable.
( With inputs from IANS )