Nauru's Government has confirmed its police force is investigating an alleged assault of a refugee child.

Reports emerged yesterday a six-year-old girl was allegedly sexually abused, with her father, an Iranian refugee, among those who claimed to have witnessed the perpetrator in the act.

Police statements obtained by the ABC allege the supposed offender was known to the girl and he did something she described as "not the right thing to do to a child".

In a statement issued by the Nauru police force today, officials stated no Nauruan national was involved in the alleged incident.

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"It would be inappropriate to provide details of an ongoing investigation," it read.

"However we can confirm that both the alleged victim and the person accused by the family of the alleged victim are from the refugee community on Nauru."

Police officials also criticised media outlets for their coverage of the alleged incident, stating that officers were acting "according to normal procedures".

The Nauruan Government also issued a statement on social media, asking journalists and "those making uninformed comments" to allow police to continue carrying out due process.

A spokesperson for Australian Immigration Minister Peter Dutton said the Minister was aware of the alleged assault.

"The matter is under investigation and is a matter for the Nauruan Police Force," they said in a statement.

But the father of the alleged victim said not enough action had been taken.

He told the ABC he had many questions for authorities, but could not could not get answers on why the alleged offender had not been taken into custody.

"After two days, three days, four days, that man is free," he said.

"They didn’t arrest him ... that man is free and living in the community and living with other children in the camp, in the refugee camp."

A contact from within the refugee community on Nauru said the girl's parents lived on the island in a house provided by the Government.

They said it was about 8:00pm when the mother noticed her daughter was missing and, after searching with her husband, allegedly found their daughter "in bushes with a naked guy".

"The parents are in a horrible situation," the statement said.

"They are scared and frightened."

10 reports of sexual assault in detention

The alleged incident is the latest in a series of sexual assaults on Nauru, which have involved both asylum seekers and processed refugees.

Immigration spokeswoman Cheryl-Anne Moy told Senate estimates last year there had been 10 reports of sexual assault involving children in immigration detention in the period between September 2013 and September 2015.

Ms Moy said five of those reported assaults related to a lone incident.

There were nine reported sexual assaults of adults in immigration detention on Nauru over the same period, as well as 82 allegations of physical abuse involving children.

Outside the centre, there have been 10 reports of sexual assault against processed refugees between May 2014 and September 2015.

Ms Moy said "a number" of the sexual assaults had been reported to Nauruan police.