French President Francois Hollande said the two hostage takers were terrorists who had pledged allegiance to Islamic State
Two men who took several people hostage in a church in France's northern Normandy region have been "neutralised", a police source said on Tuesday.
It was not immediately clear if the assailants had been killed or taken alive during a police operation.
The men armed with blades had taken several people hostage in a church in France's Saint-Etienne-du-Rouvray.
Police say the priest taken hostage was killed with a blade. The source said it looked like the priest had had his throat slit. French ministry says the second hostage is also fighting for his life.
French President Francois Hollande said the two hostage takers were terrorists who had pledged allegiance to Islamic State and that the war against the group must be fought "by all means."
"We are faced with a group, Daesh (Islamic State), that has declared war against us. We must lead this war, by all means, while respecting the rule of law," he told reporters at the scene in Saint-Etienne-du-Rouvray.
The attack took place during morning mass at the Saint-Etienne parish church, south of Rouen in Normandy. Five people were initially taken hostage. The hostages had included a priest, two nuns and two worshippers according to BFM TV.
There were no immediate details on the identity or motives of the two assailants but the investigation was handed to the anti-terrorist unit of the Paris prosecutor's office.
The attack is the latest in a string of deadly assaults in Europe, including the mass killing in Nice on Bastille Day and four incidents in Germany. Many of the attacks have had links to Islamist militants.
The Archbishop of Rouen identified the slain priest as Father Jacques Hamel. The Vatican condemned what it said was a "barbarous killing".
The Islamic State group said the two assailants who stormed the church were its "soldiers," an IS-linked news agency reported.
"The perpetrators of the Normandy church attack are soldiers of the Islamic State who carried out the attack in response to calls to target countries of the Crusader coalition," the Amaq news agency said, citing a "security source".