An 84-year-old priest was killed and four other people taken hostage by two armed men who stormed his church in a suburb of Rouen in northern France.
The two attackers, who said they were from the so-called Islamic State (IS), slit Fr Jacques Hamel’s throat during a morning Mass, officials say.
Police later surrounded the church, in St-Etienne-du-Rouvray, and shot dead both hostage-takers.
One of the hostages is in a critical condition in hospital.
President Francois Hollande, visiting the scene, said the attackers had committed a “cowardly assassination” and France would fight IS “by all means”.
Pope Francis decried the “pain and horror of this absurd violence”.
UK Prime Minister Theresa May branded the attack “sickening” and offered her condolences to the people of France.
One attacker is reported to have been known to French police, and had tried to enter Syria last year.
Police special forces raided a house in Saint-Etienne-du-Rovray in the aftermath of the attack, and French prosecutors earlier said one person had been arrested.