Refugee advocates say a pregnant refugee from Iran and her husband were flown by air ambulance from Nauru to Australia on Wednesday.
They say two other families from Iran and one from Bangladesh were also flown from Nauru to Australia on Wednesday with at least two children.
Meanwhile, the government of Nauru has issued a statement about an Australian media report in which it said a refugee allegedly poisoned a child in an attempt to be transferred to Australia.
The government said it condemns the actions of refugee parents who put their children at risk by intentionally hurting them, ordering them not to eat or drink, or encouraging them to self-harm.
It said Nauru continues to place a high priority on the welfare of all refugees and works closely with the Australian government to ensure they receive the highest level of care.