Detectives are treating the fire at the historic Crooked House pub as arson, Staffordshire Police have said.
Some 30 firefighters were needed to tackle the blaze at the pub in Himley, near Dudley in the West Midlands, on Saturday evening and it was demolished two days later.
The force said on Wednesday evening: “This fire has shocked and upset so many given the, albeit not listed, cultural importance and heritage of the building.
“This is not lost on us and a robust investigation using all available information and forensic opportunities is being carried out.”
The police said they have spoken to the owners of the pub and continued to engage with them.
The force added that speculation is extremely unhelpful and could hinder its investigation.
A joint investigation is being carried out by the police and Staffordshire Fire and Rescue Service.
Police are liaising closely with fire investigators, who have confirmed the cause of the fire cannot currently be determined, but the force said they are following up on a number of lines of inquiry.
A specialist fire investigator has examined the scene to try and determine the cause of the fire.
The fire service also revisited the grounds on Wednesday with a specialist accelerant detection dog to investigate further.
Detective Chief Superintendent Tom Chisholm, head of specialist crime at Staffordshire Police, said: “We understand the significance of this much-loved building, and the upset and anger felt by many, so want to reassure you we’re doing all we can to understand more about what happened and who was responsible.
“There is lots of misinformation circulating within communities and online, and this is unhelpful. We’re trying to provide accurate and timely updates, but as I am sure you can appreciate there is a lot of work and liaison with a number of partners which needs to be completed, and this takes time.
“There are also certain things that police and fire do not have the powers to deal with, the decision around partial demolition of the building, for example, when the scene was handed back to the owner.
“We are working hard with our fire colleagues to understand the cause of the fire and are in contact with the landowner, we will keep you updated with any further significant developments.”
Anyone with information is encouraged to get in touch with the police via 101 quoting incident 761 of August 5.
People can also call Crimestoppers on 0800 555 111 or use the Live Chat on the Staffordshire Police website.