Update 3.15pm: One person has been arrested in France after an attack on a church in which an elderly priest was killed.
Update 2.04pm: The so-called 'Islamic State' group has claimed responsibility for the attack in France in which two people killed an 84-year-old priest.
The claim, which came in a statement published by the IS-affiliated Aamaq news agency, said the attack was carried out by "two soldiers of the Islamic State."
Update 1.15pm: French president Francois Hollande has suggested that the so-called 'Islamic State' group is behind the church attack in Normandy that left an 84-year-old priest dead.
Mr Hollande called the incident a "vile terrorist attack" and said it is another sign that France is at war with 'IS', which has claimed a string of attacks on France.
"We must lead this war with all our means," he said.
Mr Hollande expressed support for all France's Catholics but said the attack targets "all the French."
Earlier: Two attackers killed an 84-year-old priest by slitting his throat before being shot and killed by police after they seized hostages in a church in Normandy.
Archbishop Dominique Lebrun of Rouen confirmed the identity of the priest as Father Jacques Hamel, 84.
Another person inside the church near the city of Rouen was seriously injured and is between life and death, Interior Ministry spokesman Pierre-Henry Brandet said.
Police managed to rescue three people from the church in the small north-western town of Saint-Etienne-du-Rouvray, said Mr Brandet. The hostage-taking occurred during morning Mass, he told reporters.
The French president has suggested the so-called Islamic State group is behind the attack.
Police said two attackers entered Father Hamel's church in the small Normandy town of Saint-Etienne-du-Rouvray, slit his throat and took hostages before being shot dead by police.
In a statement from Krakow, Poland, where Pope Francis was visiting, Archbishop Lebrun said: "I cry out to God, with all men of good will. And I invite all non-believers to unite with this cry ... The Catholic Church has no other arms besides prayer and fraternity between men."
The identities of the attackers and motive for the attack are unclear, according to a security official.
Tuesday's slaying inside a church "is obviously a drama for the Catholic community, for the Christian community," Mr Brandet told reporters.
French president Francois Hollande and interior minister Bernard Cazeneuve were heading to the town.
Mr Brandet, speaking on BFM TV, said the RAID special intervention force was searching the church and its perimeter for possible explosives and terrorism investigators had been summoned.
The hostage-takers entered the church armed with knives shortly before 10am local time (9am Irish time), said French media sources.
As the situation developed, officers from the elite anti-terrorist Raid squad were called in to assist local police.
A number of shots were heard over a period of around 15 seconds as the incident came to an end around 40 minutes later.
Anti-terrorist authorities in Paris have opened an inquiry into the hostage-taking.
Eulalie Garcia, who works in a beauty parlour, is on the same road as the church, and told reporters that she knew the 92-year-old priest, who had taught her the catechism as a young girl.
"My family has lived here for 35 years and we have always known him," she said. "He was someone who was treasured by the community. He was very discreet and didn't like to draw attention to himself."
She said she was very shocked by the death of the priest, who lived opposite his church. "It can happen to anyone," she said.
The area around the church remained cordoned off and the old town was out of bounds.
French newspaper Le Figaro reported that the church was suspected to have been on a list of Catholic places of worship in the area around Paris drawn up as possible targets by Sid Ahmed Ghlam, an Algerian student arrested last year on suspicion of murdering a mother-of-one during a botched attempt to attack a church in Villejuif.
In an impromptu press conference at the scene, Mr Brandet said that a careful investigation of the church building was being conducted by anti-terrorist officers, using sniffer dogs to ensure that no bombs had been left behind by the hostage-takers as booby-traps.
The scene was being investigated by forensic officers, in an operation which was expected to last throughout the day, he said.
Mr Brandet said: "I will not talk about the motives of these individuals.
"I cannot tell you more about the persons who have been seriously injured and who have been assassinated, for the simple reason that investigations are ongoing and the explosive sniffer dogs are carrying out their work.
"We face a dramatic situation that we have to face up to once again, less than two weeks following the Nice tragedy."
Mr Brandet was unable to say whether the hostage-takers had firearms.
"The investigation will continue throughout the day," he said.
"We are at the start of the operation. The priority was to make sure we got the assailants and rescued as many hostages as possible.
"Unfortunately the toll has been extremely high. One person was assassinated and another was seriously injured."
French prime minister Manuel Valls said in a message on Twitter: "Horror in the face of the barbaric attack on a church in Seine-Maritime. All of France and all Catholics are bruised. We stand together."
France is on high alert after an attack in Nice on Bastille Day - July 14 - that killed 84 people and a string of deadly attacks last year claimed by the Islamic State group that killed 147 others.
The country is also under a state of emergency and has extra police presence in the wake of the Nice attack in which a man barrelled his truck down the city's famed Promenade des Anglais, mowing down holiday crowds.
Islamic State extremists have urged followers to attack French churches and the group is believed to have planned at least one church attack earlier.
In April 2015, an Algerian student who was arrested after shooting himself in the leg was found with heavy weapons, bulletproof vests and documents linked to Islamic State.
He is charged with killing a young woman inside her car the same day. According to French authorities, the suspect, Sid Ahmed Ghlam, was sent by the Belgian Abdelhamid Abaaoud to attack a church in Villejuif, just outside of Paris.
A cell directed by Abaaoud later carried out the November 13 attacks in Paris that left 130 people dead and the March 22 attacks in Brussels that killed 32 people.