Amnesty International has alleged many of the 400 asylum seekers detained at the Nauru centre have attempted suicide over prison-like conditions they face in indefinite detention.
Amnesty says its findings in a new report entitled Island of Despair are based on both desk research and field work in Nauru between July and October this year.
It describes the detention program as a "systematic regime of neglect and cruelty."
Prime Minister Malcolm Turnbull has flatly denied their claims in an interview on the ABC.
"Well, I reject that claim totally. It is ... It is ... It ... It's ... It is absolutely false. The Australian Government's commitment is compassionate, and it's strong."
The head of the Department of Immigration and Border Protection, Michael Pezzullo, has also rejected the claims.
"I refute categorically, both on behalf of my own department and by way of explaining government policy in this regard ... It's not the Australian government's position nor the position of this department that we flout any laws, international or otherwise."
The Nauru government has not responded directly to the Amnesty report.
But it has criticised an ABC television story that made similar allegations and quoted children on Nauru.
Under Australia's immigration policy, asylum seekers intercepted trying to reach the country by boat are sent for processing at a camp in Nauru or to Manus Island in Papua New Guinea.
They are not eligible then for resettlement in Australia.
The Government insists it is trying to convince people not to undertake the dangerous boat journey.
Independent senator Nick Xenophon says the Government has to strike a balance.
"It's important that you deter the flow of boats to this country. But that doesn't mean that we have to be cruel about it. It's very important that there are safeguards for people's rights, for their human rights."
Independent senator Derryn Hinch has questioned the reliability of Amnesty's report.
"Amnesty International's position is pretty straight, pretty consistent and, I think, fairly exaggerated on a lot of things. I took off my little barbed wire Amnesty International tag when they started defending convicted killers in the United States some years ago."
The Turnbull Government has been trying to organise resettlement of the asylum seekers in other countries.
But, so far, it has only struck a deal with Cambodia, an option that proved very unpopular with refugees.
Australia is also facing pressure over its detention centre in Papua New Guinea that holds 823 men.
In April, the PNG Supreme Court ordered its closure.
The Prime Minister has declined to comment on the discussions with further countries about resettling the refugees.
Those talks come as Australia has agreed to be a third country for some Central American refugees from Honduras, El Salvador and Guatemala who have reached Costa Rica.
The Department of Immigration has told parliament no refugees have arrived yet but they could begin arriving anytime now.
The department says it is yet to be determined how long that program will run.
