The incident took place near Lal Haveli -- the residence of Railways Minister Sheikh Rashid in Rawalpindi -- on Saturday.
All of them including the family head, Waseem, his two daughters Javeria, 10, and Arham, 11, were shifted to the hospital after the incident.
DSP City Ejaz Shah said it was too early to determine the motive behind the incident.
He said all five members of the family were found in an unconscious state. Ruqqaya, the mother, along with her son, Ibrahim, breathed their last at the district headquarter hospital.
Battagram youth commits suicide after being sexually assaulted, blackmailed
Waseem, as well as, Javeria and Arham are said to be still in critical condition.
Authorities say that the family added poison to tea and consumed it.
Local police said that they have taken the bottles of poison found from their home into their possession.
DSP Shah said that a Pakistani national living in Canada had allowed the family to live at his residence and look after it.
Earlier on March 26, a young student took his own life after being sexually assaulted and blackmailed by two men in Battagram district of Khyber-Pakhtunkhwa (K-P).
A*, an orphan, committed suicide on March 14 in Shingli Bala village of the district.
An initial investigation by police revealed that A* took his own life after being blackmailed by two men, who had sexually assaulted him and filmed the act as well.
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