However, his government will look into the claims, Mr Baron Waqa told Channel NewsAsia on Tuesday (Aug 16).
Last week, The Guardian published more than 2,000 case reports detailing allegations of abuse faced by asylum seekers being processed by the Australian government on the remote Pacific Island of Nauru.
They include reported incidences of assaults, sexual assaults and self-harm - many involving children - between 2013 and 2015.
When asked about reports of alleged abuse of asylum seekers on Nauru, President Waqa said the allegations have been played up by media and "a lot of them have just been made up".
"There are people who are advocates and those sorts of people who are wanting to discredit the programme, or are always quick to put out negative stuff in the media," he said. "We will continue to get to the bottom of it but as far as Nauru is concerned, we look at every individual complaint there is."
More than 400 asylum seekers are being held in Nauru, one of several controversial offshore detention centres run by Australia.
This latest leak of documents has prompted fresh calls for a parliamentary inquiry into how the centres are run.
On Monday, more than 100 former and current employees at the Nauru and Manus Island detention centres published an open letter saying "the only way to secure the safety of refugees and asylum seekers in these locations is to bring them to Australia immediately."
However, Australia's Department of Immigration and Border Protection has said "many of the incident reports reflect unconfirmed allegations or uncorroborated statements and claims - they are not statements of proven fact".
"The Australian Government continues to support the Nauruan Government to provide for the health, welfare and safety of all transferees and refugees in Nauru," it said in a statement on Aug 10.
Nauru is the world's smallest island republic, with a population of about 10,000 people. The Australian processing centre there was reopened in 2012 and in 2015, The Guardian reported Australia was paying Nauru an estimated A$29 million in monthly visa fees, in addition to operating costs.
"It's going very, very well. I think we've done our best to handle all the problems," said President Waqa. "Of course there's always resentment and things coming from asylum seekers and refugees.
"Nauru is a unique place, we look after people, we welcome them and we go out of our way to make them welcome and look after them," he added.
President Waqa was in Malaysia to join a panel discussion on creative approaches to governance along with Malaysian Prime Minister Najib Razak, Thai Prime Minister Chan-ocha, the King of Swaziland, Mswati III, and the vice-president of the Maldives, Abdullah Jihad, at the International Conference on Blue Ocean Strategy.