Armed officers were seen swarming the residential street, with around 70 people moved to an emergency temporary rest centre in the nearby Snuff Mill Harvester restaurant.
Police set up a white tent at the scene of the blast, and a cordon was later extended to cover the corner of Froomshaw Rd.
Police said the incident was not being treated as terror-related, and that a major incident had been declared.
Ebbs said: “A woman and a man have died at the address and we’re treating the explosion as suspicious. Their families have been updated and are being supported by specially trained officers, and our thoughts are very much with them.
“Three people, a man, a woman and a child, were taken to hospital to be treated for minor injuries.”
Police are making inquiries at a separate property in Speedwell, 5km from the scene, which was linked to the man who died.
One resident, Bradley Shepherd said he had “jumped out of bed” after hearing a “large explosion”.
He told the BBC: “There was nothing immediately that I could see, but within minutes the police were arriving, attending the property.
“We had all emergency services there within 10 minutes, armed police. Within maybe about 15 or 20 minutes, once they had it cordoned off, they were instructing all the neighbourhood – the majority are probably 60-plus years of age – to actually evacuate their properties and take residence in the local Harvester.”
A major incident is defined by the College of Policing as “an event or situation with a range of serious consequences, which requires special arrangements to be implemented by one or more emergency responder agencies”.
A police spokesman said: “Given the recent change to the UK threat level, we would like to reassure the public from the outset that we are not treating this as a suspected terrorist incident. We ask people not to speculate around the circumstances and continue to encourage the public to avoid the area while emergency services respond to this incident.”
Police said the cordon had been put in place “as a precaution to help keep the public safe”. There was not believed to be any significant damage to other properties, they added.
Al al-Maghrabi, a Bristol city councillor said: “I am devastated to hear the news this morning that two residents have lost their lives following an explosion on Sterncourt Rd in Frenchay. My thoughts are with their families at this incredibly difficult time.
“Avon and Somerset Police have confirmed that they are not treating this as a terrorist incident, and that they are not looking for anyone else in connection with the incident at this stage.
“I want to say a huge thank you to the Harvester for opening their doors to evacuated residents and providing meals and drinks during this difficult time.”
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