A knifeman stabbed a French police chief to death in front of his Paris suburb home late on Monday and his partner's body was found inside, officials said.
Accordng to the Islamic State's Amaq news agency, the killings were carried out by a "fighter" belonging to the militant group.
The unidentified attacker repeatedly knifed the 42-year-old commander in the stomach before barricading himself inside the house, an Interior Ministry spokesman said.
He was shot dead by members of an elite police unit after negotiations failed.
A judicial source said the anti-terrorism unit of the prosecutor's office had been handed the investigation because of comments made during lengthy exchanges between the assailant and negotiators, but gave no further details.
"Source to Amaq agency: 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.
President Francois Hollande will hold an emergency meeting over the killings early Monday morning, his office said before Amaq posted its statement, underscoring the seriousness with which the Elysee presidential palace is treating the incident.
If it is confirmed Islamic State was behind the murders, it would be the first militant strike on French soil since the government imposed a state of emergency after the multiple attacks on Paris in November that killed 130 people.
The killings took place as France, a founder member of the US-led coalition waging air strikes against Islamic State, was already on high alert for terrorist attacks during the Euro 2016 soccer tournament which began on Friday.
Islamic State's claim that one of its "fighters" carried out the evening attack came a day after the Islamist militant group said it was responsible for the shooting that killed at least 49 people in a massacre at a gay nightclub in Orlando, Florida.
The knifeman struck in the Paris suburb of Magnanville, about 50 km (30 miles) northwest of the French capital and about 20 km (12 miles) from Les Mureaux where the police commander was stationed.
He stabbed the police commander nine times in the stomach before forcing his way into the house and taking the officer's partner and three-year-old son hostage.
"Negotiations were unsuccessful, a decision was made to launch an assault," Interior Ministry spokesman Pierre-Henry Brandet said.
Commandos from the RAID police unit stormed the house and found the woman's body. The young boy was rescued "in shock but unharmed", a prosecutor said.
Officials have not revealed the identity of the 42-year-old officer.