The Islamic State (IS) group said Tuesday that two of its "soldiers" had attacked a church in northern France, slitting a priest's throat, stunning a country already shaken after a series of jihadist attacks.

The hostage drama in the Normandy town of Saint-Etienne-du-Rouvray comes on the heels of another IS-claimed massacre in the French Riviera city of Nice less than two weeks ago, which left 84 people dead.

President Francois Hollande said the two men who stormed the Catholic church in Normandy before killing its elderly priest had claimed allegiance to IS before being shot dead by police.

Shortly afterward, the IS-linked Amaq news agency, citing a "security source," said the perpetrators were "soldiers of the IS who carried out the attack in response to calls to target countries of the Crusader coalition."

The two attackers stormed the church during morning mass, taking the five people inside hostage, including the priest, interior ministry spokesman Pierre Henry Brandet said.

He said the church was surrounded by police from the elite BRI unit, which specializes in kidnappings, and that "the two assailants came out and were killed by police."

The priest died after his throat was slit, sources close to the investigation told AFP.

The archbishop of the nearby city of Rouen, Dominique Lebrun, identified the priest as 84-year-old Jacques Hamel.

Three of the hostages were freed unharmed, and another was fighting for his life, said Brandet.

Hollande appealed for "unity" in France, where political blame-trading has poisoned the aftermath of the Nice attack, the third major strike in the country in 18 months.

"The threat remains very high," said the president. "We are confronted with a group, Daesh, which has declared war on us," Hollande said, using an alternative name for IS.

"We have to wage war by every means, [while also] upholding the law, which is because we are a democracy."

The Paris prosecutor's office said the case was being handled by anti-terrorism prosecutors.

Pope Francis voiced his "pain and horror" at the "barbaric killing" of the priest.

France has been a prime target of IS, which regularly calls for supporters to launch attacks against the country, a member of the international coalition carrying out airstrikes against the jihadist group in Iraq and Syria.

Attacks in Belgium in March and in Germany this week have also increased jitters across Europe.