An asylum seeker has died on Christmas Island after he escaped from the Australian-run detention centre on Saturday morning.

Key points: Immigration Department says detention centre staff reported a man missing on Saturday morning

Immigration Department says detention centre staff reported a man missing on Saturday morning Australian Federal Police found man's body on Sunday

Australian Federal Police found man's body on Sunday Refugee Action Coalition says man who died was Iranian Kurd in his 30s

Australian Federal Police found the body on Sunday after a day-long search for the man.

The Department of Immigration and Border Protection confirmed the escape and death on Sunday evening and said the matter was being investigated by the coroner.

The department said in a statement that service provider staff reported an "illegal maritime arrival" had escaped from centre on Saturday morning.

"The matter was referred to the Australian Federal Police who commenced a search and discovered a deceased person today," the statement said.

The Refugee Action Coalition said the detainee was an Iranian Kurdish man in his 30s.

Border protection officials said the situation remained calm at the detention centre.

Christmas Island Shire president Gordon Thomson said he was angry local residents had been told nothing about how the asylum seeker escaped from the local detention centre and died.

Mr Thomson said he had contacted the Immigration Department on Sunday morning but it did not tell him anything.

"I am very sad to hear that someone has died," he said.

"I want that recorded and I am very, very disappointed that the department has allowed rumour to spread through the community over the last two-and-a-half days, without providing any information about what underpins that rumour."

Mr Thomson said the escape had triggered an element of panic in the community.

"That's why I wanted the information from the department [on Sunday] morning so we could put people's minds to rest or inform them at least what's going on and any precautions they might need to take," he said.

The centre has been in operation since December 2008, but earlier this year the federal budget outlined the winding down of detention facilities on Christmas Island.

The budget included plans to close the Phosphate Hill and Construction Camp facilities.

It also said the main North West Point centre — where the asylum seeker who was found dead on Sunday went missing from — would only be used as a contingency from 2016.

In the five months after the announcement, the number of detainees at the detention centre tripled to 221, with one detainee claiming that asylum seekers were being detained alongside criminals waiting to be deported.