Terry Good, 12, his sisters Alison, 10, and Nicola, 8, and their brother Patrick, 6, were found huddled together in a first-floor bedroom at the family's home in the Sholing area. Neighbours had earlier heard them screaming "Mummy, Daddy, help us please".
Their sister, Kelly, 14, was badly burnt, but is in a stable condition in hospital.
She and her parents, Melvin and Bev, escaped from the house and neighbours stopped Mr Good, a building worker, from going back into the flames in a rescue attempt that would have cost him his life.
People living on the council estate said yesterday that the family had been threatened in recent weeks and one spoke of a group of youths standing near the blazing house shaking their fists and shouting "burn you bastards, burn".
Police refused to confirm the reports, but Detective Superintendent Peter Neyroud said: "We have launched a major inquiry. At present the fire is being treated as suspicious until our investigations can confirm or deny this."
He said that he wanted to hear from anyone who saw a vehicle pulling up near the house between midnight and 2am yesterday morning or witnesses who saw anybody going to or from the house at that time.
He added: "This is an appalling incident which cuts short the lives of four young people. A fifth youngster is severely injured and the remainder of the family are traumatised."Reuse content