A man with psychiatric problems fatally stabbed his mother and sister in the Paris suburb of Trappes on Thursday and seriously wounded a third person, French Interior Minister Gerard Collomb said.
The 36-year-old launched his attack in a street in broad daylight before taking refuge in a house. He was shot dead by police when he ran towards them in a threatening way, the minister said.
"It appears the criminal had serious psychiatric problems," Collomb told reporters in Trappes.
"He was known (to police) for advocating terrorism but it seems he was a disturbed person rather than someone who could respond to calls for action from terrorist organisations like Daesh," he said, using the Arabic acronym for Islamic State.
Collomb said counter-terrorism prosecutors were not at this stage in charge of the investigation but were following it closely.
Trappes is a low-income town located in Paris' affluent western suburbs.
Dozens of radicalised youths from the town of about 30,000 habitants have left for Syria.
Islamic State leader Abu Bakr al-Baghdadi, in his first purported speech in nearly a year, called on followers to fight on despite battleground defeats, according to an audio recording posted on the group's media outlet on Wednesday.
Islamic State swiftly claimed responsibility for the attack but provided no evidence of a link to the knifeman.
BFM TV said the attacker shouted "Allahu Akbar", but police could not confirm this, and they said investigators were looking into whether this was a family quarrel.