PARIS — A man on a terrorism watch list fatally stabbed his mother and sister, and seriously wounded another person, in a Paris suburb on Thursday, before the police shot him to death, the authorities said.

As of Thursday night, officials said they believed that the killing was related to family issues, which Frédéric de Lanouvelle, a spokesman for the Interior Ministry, described as “pretty tense.” Mr. de Lanouvelle, speaking on BFM television, did not identify the assailant but said he was 36.

The Amaq News Agency, which is linked to the Islamic State, said the group had claimed responsibility for the knife attack. The claim was made in language indicating that the attacker was inspired by the group’s ideology, rather than being a core member of it.

But Interior Minister Gérard Collomb said the assailant was “more someone unstable rather than someone who would be following the instructions of terrorist organizations.” He described the attacker as having “important psychiatric problems.”