A man flagged by French authorities as a suspected radical has killed his mother and sister and seriously injured another woman in a knife attack that was quickly claimed by Islamic State.

Police shot and killed the man, whose motives were not immediately clear.

Authorities did not rule out a family dispute and prosecutors were not immediately treating the attack as a terrorism case.

Three French officials identified the two people killed in the attack in Trappes as the mother and sister of the attacker.

The third victim, a passer-by who was gravely injured in the attack, was also a woman, one of the officials said.

IS, via its Aamaq news agency, claimed responsibility.

The agency said the attack in Trappes was motivated by calls from the IS leadership to attack civilians in countries at war with the extremist group.

Hours earlier, IS leader Abu Bakr al-Baghdadi urged followers to attack enemies everywhere by all means, including in knife attacks.

Police officials said the man was flagged in a government database of suspected religious and political extremists.