The Amaq news agency of Isis said the Islamist militant group is responsible for the fatal stabbing of a local police chief in front of his home in an outer Paris suburb.
"Islamic State fighter kills deputy chief of the police station in the city of Les Mureaux and his wife," Amaq said on its news website.
The assailant, who barricaded himself inside the police commander's house, was shot dead by members of an elite police unit, officials said.
Police also found the body of a woman in the house and a surviving 3-year-old boy, the spokesman for the Interior Ministry, Pierre-Henry Brandet, said on BFM TV minutes after the elite RAID unit stormed the house.
The woman was "most probably the wife" of the commander, prosecutor Vincent Lesclous told reporters.
Shortly after the attack, Lesclous said: "We have no certainty about the motivations" of the attacker.The killings took place in the Paris suburb of Magnanville, about 50km northwest of the French capital and about 20km from Les Mureaux where the officer was stationed.
French officials said anti-terrorism prosecutors were investigating the attack.
Amaq news agency cited an unnamed "source" as saying an Isis fighter carried out the attack, but the extremist jihadist group has not officially claimed responsibility.