French President Francois Hollade has arrived at the scene of today's hostage siege in Saint-Etienne-du-Rouvray, in which a priest was killed.
President Hollande met masked members of the police and other emergency service workers.
Pope Francis is feeling "the pain and horror of this absurd violence" following the killing of a priest at a church in France.
The Vatican condemned the "barbarous killing", saying the Pope was horrified by the news.
"We are particularly shocked because this horrible violence took place in a church, in which God's love is announced," Vatican spokesman Father Federico Lombardi said.
He said the Pope "condemned in the most radical way any form of hate".
The priest killed in the siege on French church has been named.
The Catholic Church in France confirmed the death of 84-year-old Father Jacques Hamel.
Born in the Rouen area, Father Hamel was ordained in 1958 and was assistant priest in the parish of St Etienne.
Archbishop of Rouen, Dominique Lebrun, who cut short a visit to Poland to return to his diocese, said: "I'm calling out to God, alongside all good-willed men. I'm inviting all non-believers to unite behind this call.
"The only arms which the Catholic Church can take up are prayer and brotherhood between men.
"I'm addressing the hundreds of young people who are the true future of humanity.
"I'm asking them to not lower their hands when faced with violence and to become apostles of the civilisation of love."
The Archbishop of Canterbury has tweeted 'pray for France' after the news a priest was killed during a church siege in Normandy.
The Vatican has condemned the killing of a priest in a church in Normandy as "barbarous".
It said the attack was "even more heinous" because it happened in a scared place.
A woman taken hostage in a French church is fighting for her life, officials said.
Pierre-Henry Brandet, spokesman for the interior ministry, said the woman, believed to be a member of the congregation, was "between life and death".
She was one of five hostages - including a priest and two nuns - held in Normandy.
The elderly priest killed after being taken hostage with four others in a church in Normandy was "treasured by the community".
He was killed with a knife with some reports stating he had his throat slit in the attack.
The two hostage takers - who also held two nuns and two members of the congregation - were shot dead by police.
Eulalie Garcia, who works on the same road as the church, said she knew the priest.
"My family has lived here for 35 years and we have always known him. He was someone who was treasured by the community."
French terror police are taking over the investigation into a church siege in which a priest was killed.
Five hostages - including a priest, two nuns and two worshippers - were held in Saint-Etienne-du-Rouvray, south of Rouen, in Normandy.
The hostage takers - two men armed with knives - were shot dead by police.