The immigration department says centre operators are working to bring a “disturbance” at the facility under control.
However, Greens senator Sarah Hanson-Young told Sky News the centre was in “meltdown” and a refugee advocate said sections of the centre had been set on fire.
NZ Labour MP Kelvin Davis, who recently visited the island, said he had been in touch with a New Zealander in detention on the island.
Detainees had taken over the centre and guards had retreated, the MP had been told.
He claimed the riots began when a detainee who had asked questions about the death of the man was assaulted.
“They have put holes in the walls, so even if they are rounded up and put back in the cells they actually can’t be locked up,” Mr Davis told ABC Radio.
Refugee Action Coalition spokesman Ian Rintoul said fires had been started in some sections of the detention centre.
“The canteen has been burnt down,” he told AAP.
NZ detainee Lester Hohua said convicted criminals with cancelled visas like him had joined forces with asylum seekers.
He said no one wanted to be locked up any more.
“It all went haywire,” Hohua told ABC Radio.
A coroner will investigate the death of the Iranian Kurdish asylum seeker, named by refugee groups as Fazel Chegeni.
Opposition immigration spokesman Richard Marles described the man’s death as a tragic incident.
“It is important we determine exactly what happened and what the circumstances of his death were,” he said in a statement.
Former immigration minister Scott Morrison said the death was a disturbing and distressing event.
The department said it would not be appropriate to make further detailed comments on matters subject to ongoing operations.
No injuries had been reported at the centre and any criminal offences would be referred to police, the department said.
Make your contribution to independent news
A donation of any size to InDaily goes directly to helping our journalists uncover the facts. South Australia needs more than one voice to guide it forward, and we’d truly appreciate your contribution. Please click below to donate to InDaily.