The incident took place in Bhopa area, when Mehboob Qureshi, 50, was sleeping inside his one-room house along with his wife and six children.
"While Mehboob, his wife, two sons and a daughter - aged between four and seven - died on the spot, the couple's three daughters were rushed to a hospital," inspector Sanjay Verma told reporters here, some 450 km from Lucknow.
"We are yet to ascertain whether the fire broke out accidentally, or the house was torched by someone. Locals allege the house was locked from outside at the time of the incident.
Investigations are on," he added.
According to police, the condition of the three girls - aged between 13-20 - is serious.