Dorset Police said the deaths were being treated as “unexplained” but potential carbon monoxide poisoning was the “primary line of inquiry”.
The force said the families of those who died have been informed and the coroner has been notified.
Speaking on Radio Solent’s Dorset breakfast programme, the town’s deputy mayor Chris Moreton said: “My main thought this morning is naturally for the families that have lost loved ones.”
Mr Moreton said he went across to the church on Ulwell Road with his wife to offer help on Wednesday morning as the residents started to arrive.
“The response of the ambulance service gives you some initial thought of the situation which I would describe as dire,” he said.
“The manner in which it happened so quickly is enough to shock anyone – thank you to those who went the extra mile.
“The [care home] staff are traumatised… we will be endeavouring to support them.”
