The Tamil family will be released from Christmas Island and allowed to live in Perth community detention as their legal bid to remain in Australia permanently is assessed.

But Immigration Minister Alex Hawke insisted the family’s status as unlawful non-citizens was unchanged, and people who arrived by boat found not to be refugees would be deported.

“The Australian government makes clear in everything we do that we are not weakening our resolve on our border protection,” he told reporters on Tuesday.

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“People can be granted temporary protection, people can be granted permanent protection if they arrive before a certain date. But if they are not found to be owed protection obligations, the expectation is that they return home and that remains our position.”

Mr Hawke said he made the “compassionate decision” to reunite the family in Perth, as their daughter Tharnicaa, who turned four last weekend, recovered from a blood infection brought on by pneumonia left untreated at the Christmas Island facility.

The family will remain there as their legal case is resolved and will not be allowed to return to Biloela, where they remain highly popular.

But Mr Hawke conceded he could grant exemptions in “extreme or compassionate circumstances” to allow the family to remain permanently.

“If there are matters that arise, I’ll consider those and make a decision … There can be many different grounds for ministerial intervention. I don’t propose to canvass them all today,” he said.

The minister claimed people smugglers kept a keen eye on developments in Australia, warning a softened approach would “restart the trade”.

He said thousands of children, including roughly 900 from Sri Lanka, were in detention when the Coalition took power in 2013.

Mr Hawke revealed there were “several outstanding pathways” for the family, including a matter before the Administrative Appeals Tribunal and an application under Section 195A he was considering.

Another was an appeal for Mr Hawke to lift a restriction barring citizenship for Australian-born children while their parents applied for temporary protection.

Both Biloela girls were born in Australia.

“If I do decide to lift the bar, they will be able to make those applications. The remaining child will make that application and that would be assessed against the criteria,” he said.

Mr Hawke confirmed that Tharnicaa being granted citizenship could change the dynamic for her parents’ claim to permanent residency.

“If a child is found to be owed protection obligations, that then will impact the immigration status of family members here in Australia,” he said.

Deputy Labor leader Richard Marles said “common sense” ministerial discretion should have been used far sooner, avoiding a $6.7m hit to the taxpayer.

“They should never have been put in a position of being placed on Christmas Island … given the decision that‘s now being made, it begs the question as to why this didn’t happen a long time ago,” he told the ABC on Tuesday.

In question time after Mr Hawke’s press conference, Labor leader Anthony Albanese demanded to know why the government would not allow the family to “go home to Bilo(ela)”.

Acting Prime Minister Michael McCormack said immigration decisions were “never easy” but said Labor had put 8500 children in detention during its time in power.

“It’s a bit rich, and I will not be lectured to by Labor,” he said.

“I was here when, sadly, those people who tried that risky voyage were dashed up on the rocks and did not survive that. We do not know how many people lost their lives attempting to make that risky voyage.”

The family has been detained on Christmas Island since August 2019 when an 11th-hour court injunction prevented their deportation to Sri Lanka.