Prime Minister Binyamin Netanyahu opened the weekly cabinet meeting on Sunday by expressing condolences over the murders of six family members in Rishon Lezion over the weekend.
"I would like to express deep pain and shock over the horrifying murder of the members of the Oshrenko family. I am convinced that I speak for the entire public," Netanyahu told ministers a day after the murders were discovered.
"I have asked Public Security Minister Yitzhak Aharonovitch to update me on the progress of the investigation into solving this terrible act," he added.
The dead have been named as Ludmilla and Edward Oshrenko, both aged 56, Dimitri and Tatyana Oshrenko, 32 and 28, three-year-old Revital Oshrenko and three-month-old Natanel Oshrenko.
Earlier, Vladmir Zarinski, a friend and former business partner of the murdered father, told Army Radio that the incident was "business-related" and had been planned in advance.
Meanwhile, police were expected to receive the results of the autopsies conducted on the bodies of the family members, who were found stabbed to death in a partially burned-out apartment.
The family - two grandparents, two parents and two young children - had gathered on Friday evening to celebrate the older child's third birthday.
Police are seeking to determine whether a member of the family committed the murders before taking his or her own life, or whether a non-relative entered the apartment and stabbed the family members to death.
Early on Saturday morning, rescue services were called to the address on Rehov Nordau, after a report of a fire. Firefighters broke down the locked door and entered the home, where they discovered the six corpses.
The Central District's Central Unit was called in to lead the investigation, and a media gag order has been imposed.
All six members of the Oshrenko family will be laid to rest at the Givat Brenner cemetery at 5 p.m. on Sunday.