The murder on Friday of a police employee in a Paris commuter town was an attack on the French Republic, said Prime Minister Jean Castex.
"Once again, the Republic has been attacked. Once again, the French state has been threatened. We will not let this go by," Castex said on Saturday, speaking to reporters from the southern city of Toulouse.
The police administrative worker was stabbed on Friday by a man who walked into a police station in the Paris commuter town of Rambouillet.
President Emmanuel Macron said in response that France had again been the victim of a terrorist attack.
The attacker, a Tunisian national residing in France, was shot dead by police officers.
France's anti-terror prosecutor said he was leading the investigation because the assailant had previously scouted out the site and because of what he said during the attack.
A judicial source close to the investigation said the attacker had shouted "Allahu Akbar", or "God is greatest".
France has experienced several attacks by Islamist militants in recent years.
Bombings and shootings on November 13, 2015, at the Bataclan theatre and other sites around Paris killed 130 people, and in July 2016 an Islamist militant drove a truck through a crowd celebrating Bastille Day in Nice, killing 86.