The letter says the heat and dust is affecting those in the detention camp badly and one woman with asthma has twice become unconscious.
Ian Rintoul of the Refugee Action Coalition says the letter has been passed around the camp between asylum seekers to be signed.
"If there's one particular theme that runs through it, it's, 'How long are we going to be on Manus Island? We need an answer to when our processing is going to begin and how long we're going to be on Manus Island'," he said.
"But it details a range of things: the lack of air conditioners, the fans, the heat that the children suffer."
The asylum seekers have demanded a response from the Department of Immigration by close of business on Friday.
Mr Rintoul says if the letter is not answered by then, mass protests could follow.
"There have been hunger strikes on Manus Island already," he said.
"They do seem to indicate they're not interested in starting another mass hunger strike, but to see whether their democratic protests are a way they could get their voices heard."
On Christmas Eve, five asylum seekers were involved in a fight in the internet room at the detention centre.
Amnesty International refugee campaigner Alex Pagliaro says it is clear that frustrations are growing.
"We all know that when you put human beings into this situation, that is locking them up arbitrarily and indefinitely, they begin to crack," she said.
"An unavoidable outcome of this is tensions rise, people do damage either to themselves or in some cases to the people around them."
Amnesty says it hopes to send a team to Manus Island in February to assess conditions for itself.
Ms Pagliaro says Amnesty is waiting for departmental clearance for a late February trip.
"We will obviously be inspecting the conditions of the asylum seekers being kept there, their access to essential services," she said.
"We'll be looking at the nature of the detention - whether they are locked up 24 hours a day or whether they're granted a certain amount of freedom - and the steps taken to start the processing of their refugee claims."