Five people in all had been taken hostage. A police source said it appeared that the priest had had his throat slit.
An priest in his mid-80s was killed with a knife and another hostage seriously wounded on Tuesday in an attack on a church in northern France carried out by assailants linked to Islamic State.
Both attackers were shot dead by French police. Five people in all had been taken hostage. A police source said it appeared that the priest had had his throat slit.
Speaking at the scene of the attack in the Normandy town of Saint-Etienne-du-Rouvray, French President Francois Hollande said France should "use all its means" in its war against the militant group, against which France has launched air strikes in Syria and Iraq.
The president called it a "dreadful terrorist attack" and told reporters the attackers had pledge allegiance to IS. The IS news agency Amaq said two of its "soldiers" had carried out the attack.
"We are put to the test yet again, Hollande said. "The threat remains very high."
The attack is the latest in a string of deadly assaults in Europe, including the mass killing in Nice, southern France, on Bastille Day and four incidents in Germany.
Many of the attacks have had links to Islamist militants and IS has called for supporters to target countries that it has been fighting, mainly in Iraq and Syria.
Tuesday's attack took place during morning mass at the Saint-Etienne parish church, south of Rouen in Normandy.
The investigation was handed to the anti-terrorist unit of the Paris prosecutor's office. .
The Archbishop of Rouen identified the slain priest as Father Jacques Hamel and said he was 84, although others sources suggest he was born in 1930. The Vatican condemned what it said was a "barbarous killing".
French Interior Ministry spokesman Pierre-Henry Brandet told France Info radio that the perpetrators have been killed by France's BRI, an elite police anti-crime force, when they came out of the church.
Bomb squad officers aided by sniffer dogs scoured the church for any possible explosives.
Prime Minister Manuel Valls branded the attack "barbaric" and said it was a blow to all Catholics and the whole of France.
"We will stand together," Valls said on Twitter.
The attack will heap yet more pressure on Hollande to regain control of national security, with France already under a state of emergency 10 months ahead of a presidential election.
The Normandy attack came 12 days after a 31-year-old Tunisian Mohamed Lahouaiej Bouhlel ploughed his heavy goods truck into a crowd of revellers in the French Riviera city of Nice, killing 84 people. Islamic State claimed that attack.
"Horror. Everything is being done to trigger a war of religions," tweeted Jean-Pierre Raffarin, a former conservative prime minister who now heads the Senate's foreign affairs committee.
Hollande visited the scene with Interior Minister Bernard Cazeneuve, meeting members of the emergency services.
Cazeneuve has come under fire from Conservative politicians for not doing enough to prevent the Bastille Day Nice attack.
French lawmakers approved a six-month extension of emergency rule after the July 14 attack while the Socialist government also said it would step up strikes against Islamic State in Iraq and Syria.