The bodies of 39-year-old Caneze Riaz and the four girls, Hannah, Alicia, Sophia and Sayrah, aged between three and 16, were recovered in the early hours of the morning after the blaze in an end-of-terrace house in Accrington, north-west England, a spokesman said.
Lancashire Police confirmed they had launched a murder inquiry and the fire was being treated as deliberate.
A spokesman added that the house was locked from the inside when the fire broke out, apparently started by flammable material in a number of places.
"Early indications are that whoever set the fire, and carried out some other suspicious activity I can't go into at this stage, did not leave the premises," said Detective Superintendent Mick Gradwell, heading the inquiry.
The Sun tabloid reported in an early edition of its Thursday paper that Alicia Riaz, 10, called a schoolfriend, telling her: "I can smell smoke and I think we're going to die."
After her friend responded, "You've got to!", however, the line went dead.
Caneze Riaz was born to English and Pakistani parents, was described by a neighbour as a "pillar of the community" where she worked as an interpreter for local Pakistanis, was a school governor, and served as a diversity adviser to her local football club.
The father, Mohammed, 49, is in a critical condition in the specialist burns unit at Manchester's Wythenshawe Hospital. A fifth child in the family, 17-year-old Adam was in hospital receiving treatment for leukaemia, and has been informed of the tragedy.
A spokesman for Lancashire Fire and Rescue Service said he believed police were treating the blaze as "suspicious" but Lancashire Police declined to confirm this.
Fire-fighters broke in through a bay window at the front of the house before finding the bodies. Spokesman Michael Frankland said they were prevented from entering through the main door because there were several major locks on it.
"It took a little while to break in and gain access," he said. "There was a very severe house fire -- one of the worst I have seen in terms of damage."

Copyright AFP (Agence France-Presse), 2006