Jade had been on sick leave from Cashmere High School, next door to the house where she lived with her mother.
Police were trying to piece together what happened at the house between 7am, when she was last seen by her mother, and 1.25pm, when firefighters arrived after reports of smoke.
They were also trying to trace the movements of two men known to the family, aged 34 and 40, who were arrested on Thursday night.
Mr Williams called for sightings of a light green Mitsubishi Diamante station wagon that was driven by one of the men and seen on the street that morning.
Police were also searching the house where the men lived in Defoe Place, Waltham, and speaking to neighbours.
Mr Williams would not detail the charges against the men, but said they had not been charged with murder.
Police were not ruling out the possibility that other people were involved in Jade's death.
"This is one aspect of the inquiry that we're looking at but we're not closing our mind at this point in time to other avenues.''
Flowers have been placed outside Jade's house, which today remained the focus of a scene examination.
Mr Williams said the examination had been complicated by the fire and would likely continue until at least Tuesday.
Cashmere High School principal Mark Wilson today said the school community was shocked and saddened by Jade's tragic death.
He had met with the family, who were "distraught and struggling to cope with their loss'', to offer the school's condolences and support.
Mr Wilson described Jade as an outstanding student with an exemplary school record whose motivation and hard work put her near the top of her class.
"She had a quiet and shy nature, yet was also a very friendly and positive person, who was held in the highest regard by all her teachers,'' he said.
"Our school students and staff will struggle to realise and accept that we have lost this delightful young person.''
Mr Wilson said the school had been communicating with students, staff and the wider school community to notify them of Jade's death and reassure them support systems were in place.
The school had a capable counselling team while the Ministry of Education has been asked to offer the services of a traumatic incident team.
Nearby residents said smoke was seen coming out of the windows on Thursday but there appeared to be no external damage to the house.
The fire had done extensive damage to the interior of the house and the family were now staying elsewhere.
The two men arrested on Thursday were in custody until a court appearance in Rangiora on Tuesday.
