The attacker, a 25-year-old Frenchman of Moroccan origin, was later shot dead by members of an elite police unit.
A senior French policeman and his companion were killed in a Paris suburb on Monday, in the latest attack claimed by DAESH.
The attacker, who reportedly pledged allegiance to DAESH, stabbed to death the 42-year old police officer, Jean-Baptiste Salvaing. Later, he killed the policeman's female companion after holding her and their 3-year old son hostage in a lengthy stand-off.
The attacker, a 25-year-old Frenchman of Moroccan origin, was later shot dead by members of an elite police unit, officials said. The boy was rescued unhurt in an incident which would set alarm bells ringing in France as it currently hosts the Euro 2016 football tournament.
Senior police officer, Jean-Baptiste Salvaing, was stabbed several times in his stomach just after 20:30 and died outside his home. The attacker, identified by police and justice sources as Larossi Abballa, then barricaded the partner and 3-year old son in the house.
After hostage negotiations failed, RAID – an elite police unit – stormed the house after midnight.
Officers found body of the woman, a secretary at a police station in a nearby suburb, and the attacker was killed during the assault, interior ministry spokesman Pierre-Henry Brandet said.
The couple's young son was "in shock but unharmed" prosecutor Vincent Lesclous told reporters. He added that the female companion "was most probably the wife" of the commander.
French prosecutors have launched an anti-terror probe.
"The anti-terror department of the Paris prosecution service is taking into account at this stage the mode of operation, the target and the comments made during negotiations with the RAID," one source said.
Shortly after the attack, Lesclous said: "We have no certainty about the motivations" of the attacker.
French President Francois Hollande said a meeting would be held at the presidential palace Tuesday morning, declaring that "all light will be shed" on the bloody incident.
Hollande said the killings were "undeniably a terrorist act" and that the terrorist threat in France was very high.
Interior Minister Bernard Cazeneuve expressed his "infinite sadness" at the death of the police commander and his partner, who had worked for his ministry.
"The attacker was neutralised by RAID forces, who showed great composure and great professionalism and who saved the couple's little boy," Cazeneuve said in a statement.
"The inquiry opened by the justice authorities will establish the precise circumstances of this tragedy."
Sources close to the inquiry told AFP the attacker had claimed allegiance to DAESH while negotiating with police from the elite RAID unit.
The SITE Intelligence Group, based just outside Washington, cited the Amaq News Agency as saying: "Islamic State fighter kills deputy chief of the police station in the city of Les Mureaux and his wife with blade weapons near Paris."
The announcement comes days after DAESH also claimed responsibility for the deaths of 49 people at a LGBT nightclub in Orlando, Florida.