Several government MPs are reportedly urging Immigration Minister Alex Hawke to intervene in the case of the Murugappan family, who settled in the Queensland community of Biloela in 2014 on temporary bridging visas which expired in 2018.

They have been in detention ever since, despite a campaign from the Biloela to bring them back, given their importance to the community.

Bass Liberal MHR Bridget Archer said she would continue to advocate on behalf of the family.

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"I have advocated (including to the previous minister) about the family and continue to advocate for a compassionate resolution as soon as possible," she said.

Tharnicaa Murugappan, who spent her fourth birthday in a Perth hospital, was medically evacuated from Christmas Island suffering from a blood infection and pneumonia.

Acting prime minister Michael McCormack claimed that the family's detention was necessary to deter others from attempting to enter Australia via people smugglers.

But Lyons Labor MHR Brian Mitchell said this was misleading, as the minister could use his discretion in this case without changing the broader immigration regime.

"Surely the government isn't admitting it is so incompetent that billions of dollars or border security architecture can be unravelled by utilising a ministerial discretion that exists in the legislation," he said.

"If the minister can use his discretionary power to admit au pairs with Liberal links, he can use it to allow this family to resettle in Biloela where they have a community waiting for them with open arms."

The au pair matter occurred while Peter Dutton was Home Affairs Minister.

Tasmanian Labor senator Helen Polley said "let them stay".

"Enough is enough, I'm very concerned for the children's mental and social wellbeing," she said.

"A judgement should be made to allow them to return home. The Immigration Minister has that power."