The federal opposition says any new asylum seekers from Papua should have their claims assessed on the mainland, not in an offshore detention centre.
The Department of Immigration says it is investigating reports that a family of six from the troubled Indonesian province has landed on an island in Australian territory.
It comes two months after 43 Papuans landed on Australia's north-eastern tip near Cape York, sparking a diplomatic row with Indonesia.
They were detained on Christmas Island while their status was decided, but Labor's immigration spokesman, Tony Burke, says that should not happen this time.
"If you can give people much better access to their lawyers, to medical treatment, treat people with more decency by doing the processing on the mainland, and save money at the same time for the taxpayer, then that makes sense, it's the way it should be done."