RNZI reports Papua New Guinea ordered the closure of the Manus camp after the country's Supreme Court ruled the facility unlawful, leaving the fate of the 850 people held there up in the air.
Australia and Papua New Guinea each claim each other is responsible for settling the hundreds held on Manus.
The injunction, filed in Australia's High Court on Wednesday, calls for the asylum seekers to be sent to Australia and not to Nauru, Matthew Byrnes, one of the lawyers acting on behalf of the majority of those held on Manus, told Reuters.