A group calling themselves the Youth Republic of Nauru has warned refugees their situation will worsen if they stay on the island.
The veiled threat came in a letter reportedly left at accommodation and thrown over the fence of detention camps for asylum-seekers.
The letter claimed refugees were taking jobs and having affairs with local women and it warned bad things would happen if they did not leave.
There was also a warning to the local and Australian governments if they did not remove the refugees, the situation for the refugees would worsen.
The group called on local people to join in its mission.
The Nauru government earlier condemned an attack by locals on young refugees which left one Afghan teenager in hospital last month.
The country's Justice Minister David Adeang said he was determined to ensure all refugees on Nauru feel safe and welcome.