Nauruan President Baron Waqa says allegations of abuse lodged by asylum seekers and refugees are "cooked up".

More than 2,000 incident reports were published by The Guardian last week, outlining various allegations of abuse, including assaults, sexual assaults and self harm between 2013 and 2015.

The reports have prompted calls for a royal commission from the Greens and a Senate inquiry from the Opposition, but Mr Waqa told Channel NewsAsia today the media had "played up" the allegations.

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He told Channel NewsAsia's Malaysian correspondent Sumisha Naidu, who posted the interview on social media, Nauru was a "unique place where we look after people".

"These allegations are unfounded and we will continue to get down to the bottom of it," Mr Waqa said.

"But as far as Nauru is concerned, we look at every individual complaint there is and very quickly, they've been … thrown out. They have been things that are made up, a lot of them.

"It is sad because sometime media obviously play up some of these allegations which have been just cooked up and we have tried to address them.

"We have seen that a lot of them are just made up."

His comments follow those made by Australian Immigration Minister Peter Dutton, who told 2GB last week some refugees were self harming and filing false claims in an effort to get to Australia.

Mr Dutton said the allegations would be investigated by Nauruan authorities, but "some people do have a motivation to make a false complaint".

Calls for centres to be closed

President Waqa's comments also coincide with a letter signed by more than 100 former workers at the Nauru and Manus Island detention centres, who are calling for the centres to be closed.

Eliza Seaborn, who worked as a senior recreation officer with Save the Children on Nauru until October last year, is among 103 current and former detention centre staff who have signed the statement.

"I saw a lot of psychological torture, and punishment of some of the world's most vulnerable people, and Australian taxpayers are spending over $1 billion a year to do that," she said.

The statement include names of doctors, teachers, case workers, social workers and managers from government-contracted organisations such as IHMS, the Salvation Army and welfare and security service Broadspectrum.

They say Labor's proposed Senate inquiry into allegations of abuse on Nauru, in response to the leak of thousands of files from the island's detention centre, is not enough.

In a statement Mr Dutton said he understood the desire to have those housed in offshore detention centres released.

"The fact is I have to make decisions to remove people as quickly as possible, as we have done with every child in detention, but it must be done in a way that we don't see boats and deaths at sea recommence," he said in a statement.

Australia 'falling far short' of international obligations

Ms Seaborn said recommendations from previous inquiries still had not been implemented.

"There was a recommendation that a plan be put in place to bring children out of detention as soon as possible, and there are still children in there today," she said.

"It's my opinion that by having another inquiry, you're prolonging any solution and potentially avoiding accountability."

Dr Peter Young, a former director of mental health with IHMS, the government-contracted medical service on Nauru, hopes this unprecedented number of staff speaking out will make the Government listen.

Meanwhile almost 2,000 academics have signed a separate letter to the Prime Minister asking for an end to mandatory detention.

Among the group is Linda Briskman, a Professor of Human Rights at the Swinburne Institute for Social Research.

Professor Briskman told ABC's PM program leaders needed to change their messaging.

"I think people have been duped by the drownings argument and also the protection of borders argument," Professor Briskman said.

"I think we just need to give enough stories, we need to humanise asylum seekers and turn those arguments around."