Among the five deceased children was a 3-month-old infant, they said.
The fire occurred early this morning at 'Wafa' medical store located on the ground floor of a chawl in Juhi Galli on Wireless Road in Andheri, Mumbai police spokesman Ashok Dudhe said.
Eight persons were initially killed in the blaze. Later, a seriously injured woman also succumbed to her burns at a hospital, police said.
The families of the victims were staying on the first and second floors of the premises, he said.
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Prima facie, the police and fire officials suspect that because of a very small internal staircase in the chawl, the victims were trapped inside the premises and got engulfed in the fire.
"The deceased were sleeping on the floors above the medical store in the ground plus two floors chawl and could not find a passage to come out," said P S Rahangdale, chief of the fire brigade staff of Brihanmumbai Municipal Corporation.
Following the mishap, the victims were rushed to the nearby Cooper Hospital.
The deceased have been identified as - Saburiya Mozin Khan (52), Siddik Khan (35), Rabil Khan (28), Sabiya Khan (28), Mozhel Khan (8), Unnihay Khan (5), Aliza Khan (4), Tubba Khan (8) and Altaz Khan (3 months), fire brigade said.
Sabiya had sustained 45 per cent burns in the mishap and was shifted to Kasturba hospital where she succumbed.
Besides, a fireman, Avinash Shirgaokar, suffered injury in the mishap. He was treated at Cooper Hospital.
"Our fire brigade team received a call at 6.15 AM and we rushed three fire tenders, one water tanker and two ambulances to the spot," a fire brigade official earlier said, adding that the blaze was brought under control in about an hour.