CAIRO - Two Islamic State 'soldiers' carried out the Normandy church attack in France, the group's Amaq news agency said in a statement on Tuesday.
Two hostage takers killed a priest in a church in Normandy, northern France earlier on Tuesday, before being shot dead by French police.
"They carried out the operation in response to the call to target the countries of the crusader coalition," the Amaq statement said.
A source close to the inquiry later said Tuesday that French police have arrested one person in connection with the knife attack.
Earlier Tuesday, French President Francois Hollande said the two hostage takers who killed a priest in a church in Normandy, northern France, were terrorists who had pledged allegiance to Islamic State.
"Daesh has declared war on us, we must fight this war by all means, while respecting the rule of law, what makes us a democracy," he told reporters at the scene in Saint-Etienne-du-Rouvray, south of Rouen, using an Arab acronym for the Islamist extremist group.
Two assailants in the attack killed a priest with a blade and seriously wounded another hostage being shot dead by French police.
The attack took place during morning mass at the Saint-Etienne parish church, south of Rouen in Normandy. Five people were initially taken hostage.
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.
According to the French magazine Le Point
, the attackers shouted "Daesh" (the Arabic acronym for Islamic State) when entering the church.
A police source said it appeared that the priest had had his throat slit.
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."
French Interior Ministry spokesman Pierre-Henry Brandet told France Info radio that the perpetrators have been killed by France's BRI, its elite police anti-crime force, when they came out of the church.
He said that bomb squad officers aided by sniffer dogs had been scouring 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 President Francois 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 plowed his heavy goods truck into a crowd of revelers 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 and Interior Minister Bernard Cazeneuve arrived at the scene of the attack where they met with 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.