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 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 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.
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