A murder inquiry has been launched after the deaths of Andrew Broadhead, 42, and his eight-year-old daughter Kiera.
His wife Sara, 35, and another child escaped with non-life threatening injuries, through a bedroom window at the house in Ash Crescent, Stanley, in the early hours of Wednesday.
Both were treated in hospital but have since been discharged.
Police said they believed Mr Broadhead managed to get out of the house but returned in an attempt to save Kiera.
Detective Chief Inspector Nicola Bryar of West Yorkshire Police said a substance may have been poured through the letterbox, and the person responsible may have been burned in the process.
She appealed for anyone with information to contact the force.
At a press conference on Thursday, Ms Bryar said: “This is a terrible incident which has robbed a family of a husband and their youngest daughter. Following inquiries, we are now treating it as a murder inquiry.
“The seat of the fire appears to have been by the front door and we are investigating the possibility that an accelerant was poured through the letter box.
“We know that this fire took hold extremely quickly and it is possible that the person who set this fire was themselves burned in doing so.”
The family had just returned from a holiday in Spain the day before the blaze.
Ms Bryar said: “We have been conducting enquiries in line with the fire investigators at the scene and we also have scientists there.
“What we do know now is that there is a possibility that accelerants have been used at the address.
“As such, we have declared that this is now a murder investigation at this time.”
When asked what accelerants police thought may have been used, she replied: “We do not know. What we do know is that the site of the fire was the front door of the premises and we know that the fire took hold really quickly.”
She continued: “I am appealing for anybody who has any information in respect of this crime to come forward, because the fire has taken hold so quickly it’s possible that the person who has set fire to the house may have some burn injuries, may have burnt clothing.
“So if anybody has any information in respect of anybody from 4.30 yesterday morning on Wednesday 19th who has got injuries like that, please tell the police and forward.”
When asked if police believe someone outside or inside set the fire, she said: “At this moment, we do not believe that anyone inside the house is responsible for the fire.”
The victims’ family paid tribute and spoke of their shock at the tragedy.
They had been on holiday in Spain with Mr Broadhead’s parents, Alan and Jean Broadhead, and returned home on Tuesday.
Alan and Jean, both 68, were due to stay in the country longer, but cut their holiday short after the tragedy and flew home.
Alan said: “We have just come back from holiday. We were all on holiday together in Spain, but [Jean and I] stayed longer.
“We had to come back early when we heard. We’re still unpacking and expecting police to call round any minute now. It’s too soon to speak about it.
“My wife has seen people posting about in on Facebook this morning and she’s so upset. She can’t believe it’s happened.”
With his voice breaking, he added: “It is such a shock. It was very difficult to hear the news when we were abroad. We lost a son and a granddaughter.”
Dozens of bouquets of flowers had been left by the wall outside the fire damaged house in tribute.
Anyone who has information is asked to contact the Homicide and Major Enquiry Team on 101 or the indepdent Crimestoppers charity on 0800 555 111.
A JustGiving page set up to support the family has raised more than £5,000.