Turnbull was prime minister when Priya, Nades and their two young daughters were taken from Biloela in central Queensland and put into detention.
More than three years on, he now supports the family being resettled in Australia.
Turnbull acknowledged the importance of tough border security policies to stop asylum seekers making the risky journey to Australia by boat.
But he called on new Home Affairs Minister Karen Andrews to exercise some discretion.
“There’s a difference between scratching your ear and ripping it off, as my late father used to say, and you need to have a bit of subtlety, you need to have compassion, you need to have some humanity,” Turnbull told the ABC.
“That family should be back in Queensland.”
He urged Andrews to seize on the recent cabinet reshuffle to adopt a fresh approach.
“She is the new minister and she can now look at the file anew, use her discretion and bring them back to Queensland to the community that wants them, and that would be the right thing to do,” Turnbull said.
Andrews received a high-level briefing on the Tamil family when she became minister last month.
But she is unwilling to make a decision while their case for protection is before the courts.
“What I’ve done is exactly what I promised that I would do, which is look at the facts of the case,” Andrews told ABC radio.
“But this matter is before the courts at the moment, and there is nothing that I am prepared to say that will prejudice the government’s interests or the interests of that family.
“Any speculation about what will happen potentially prejudices either or both, and I’m not going to do that.”
Greens senator Sarah Hanson-Young said the family had spent more than 1000 days in detention, costing taxpayers tens of millions of dollars.
“This family have been to hell and back and it’s time this country gave them a bit of compassion and a fair go,” she said.Jump to next article