The monitoring group SITE quoted an Arabic language report on the group's Amaq propaganda agency that cited a "security source" as saying: "The executor of the stabbing operation in the city of Marseille... is from the soldiers of the Islamic State."
A suspected Islamist knifeman killed two women at the main train station in the French Mediterranean city of Marseille on Sunday before being shot dead by soldiers on patrol.
One of the victims had her throat slit by the assailant, a man with a criminal record believed to be in his 30s who witnesses said shouted "Allahu Akbar" (God is Greatest) at the start of his rampage.
French Interior Minister Gerard Collomb said about a dozen witnesses were being questioned.
"This act could be terrorist in nature but at this time we cannot confirm that," he added.
Soldiers serving in a special 7,000-strong force known as Sentinelle set up to guard vulnerable areas in terror-hit France responded to the stabbings and shot dead the attacker, whose identity remains unknown.
