An elderly priest and two armed men were killed and a person was injured in a hostage-taking incident in a church in France's Normandy region on Tuesday, President Francois Hollande said.
Rev. Jacques Hamel, 84, was killed when two men armed with knives stormed the church and took five people hostage during a morning mass at a church in Saint-Etienne-du-Rouvray area of Rouen, CNN quoted Hollande as saying.
The Islamic State said its "soldiers" slaughtered the priest and critically injured a worshipper.
"The perpetrators of the attack on a church in Normandy, France, are two Islamic State soldiers," the jihadist group's Amaq news agency said, citing an IS security source.
"They responded to an appeal to strike countries belonging to the Crusader coalition," AKI quoted Amaq as saying.
Earlier, Hollande said the attack was a "cowardly assassination" carried out "by two terrorists in the name of Daesh (the IS)".
The attackers were shot dead by the police. "The two killers came out and they were neutralized," French Interior Ministry spokesman Pierre-Henry Brandet said.
Besides the slain priest, two nuns and two churchgoers were taken hostage, BFMTV reported.
The injured hostage was "between life and death", Brandet said.
The priest's killing follows a string of violent attacks across the Europe in recent days, most of them claimed by the IS, most notably July 14 attack in the French city of Nice that left 84 dead and more than 300 injured.
France has been under a state of emergency since the November 13 Paris terror attacks last year. At least 130 people were killed and over 350 were injured in a serious of attacks.
French police told CNN that one of the church attackers had tried to go to fight in Syria last year, but had been stopped in Turkey by authorities.
He was then sent back to France and sent to prison in May 2015. Before he was released, he was placed under police surveillance and forced to wear an electronic monitoring tag.
French authorities have struggled to monitor the thousands of domestic Islamic radicals on their radar, and, in response to the heightened terror threat, President Hollande has vowed to double the number of officials charged with the task.
More than 10,000 people were on their "fiche S" list, used to flag radicalised individuals considered a threat to national security.
"Daesh has declared war on us. We have to win that war," Hollande told the media after the hostage situation was neutralised.
He also urged the public to remain unified in the face of the threat. "All people feel affected so we must have cohesion ... no one can divide us," he said.
"Terrorists will not give up on anything until we stop them."
The Paris anti-terror prosecutor has taken over the investigation into the attack, France's Interior Ministry said in a statement.
The Vatican condemned the attack, particularly the killing of the priest, calling it "terrible news". It said the Pope shared the pain and horror in response to the "absurd violence".
A statement said the violence was particularly horrific as it took place in a church, "a sacred place where the love of God is announced".
French Prime Minister Manuel Valls tweeted his horror at the "barbaric attack" on the church, and vowed a defiant response. "We will stand together," he said.
A police cordon has been set up around the scene, about 108 km northwest of Paris.