Christmas Island's administrator Barry Hasse has joined the shire president in saying not enough information was provided to locals about the detention centre riot.
Shire president Gordon Thomson has been scathing of the Department of Immigration and Border Protection's handling of the unrest, saying it had not told residents and local authorities what was going on, prompting speculation.
On Wednesday, Mr Hasse indicated he shared Mr Thomson's concerns.
"I hope there will be an agreement that there will be more information progressively made available to the community," Mr Hasse told ABC radio.
His predecessor Jon Stanhope also hit out at federal government secrecy surrounding the death of Fazel Chegeni Najad, an Iranian Kurdish refugee who was found dead outside the centre after escaping on Sunday, sparking the protests.
Immigration Minister Peter Dutton has refused to comment specifically on the death as it will be investigated by a coroner.
Mr Stanhope said if the death had been a traffic accident police would be open about it.
"It's blatant nonsense to suggest that a politician can't speak about the death of somebody within your care and control and custody," he told the broadcaster.
Long-term Christmas Island resident John Richardson told 6PR that locals knew very little about the man's death.
"However if the bloke's gone into the jungle, he's put his own life at risk," Mr Richardson said.
"We've lost lots and lots of people on Christmas Island because they've just got lost and wandered around and fallen over cliffs or got exposure."
He said most locals didn't care about what went on at the detention centre as long as it was adequately controlled, which it clearly wasn't - so security needed to be improved.
Mr Dutton says the centre's security is being reviewed and will be increased if needed.
Meanwhile, Labor has demanded an independent inquiry into the riot.
Opposition spokesman Richard Marles said there were serious questions about the government's handling of what it initially labelled "a disturbance".
"We need to know that appropriate security is in place at the centre and staff are adequately trained to deal with detainees, including those that have had visas cancelled," he said.