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 surrounded the church and shot dead both hostage-takers. French media named one of them as Adel K.
One of the hostages is in a critical condition in hospital.
President Francois Hollande, visiting the scene, in Saint Etienne-du-Rouvray, 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.
The suspect named as Adel K, aged 18, is reported to have been in custody and then placed under a control order, and had tried to enter Syria twice.
Police special forces raided a house in the suburb in the aftermath of the attack, and French prosecutors earlier said one person had been arrested.
The attack happened during morning Mass at the historic church, situated in a quiet square of St-Etienne-du-Rouvray.
A nun, who identified herself as Sister Danielle, said she was in the church at the time.
“They forced [Fr Hamel] to his knees. He wanted to defend himself, and that’s when the tragedy happened,” she told French media.
“They recorded themselves. They did a sort of sermon around the altar, in Arabic. It’s a horror”.
She said she managed to flee as they were preparing to kill him.
Elite police units, specialised in hostage-taking, surrounded the church.
President Hollande said the attackers claimed to be from the self-styled IS before they were killed by police as they came out of the church.
Three of the hostages were freed unharmed, but one remains in a critical condition, said French interior ministry spokesman Pierre-Henri Brandet.