The attack is the third in two weeks in France and Germany in which jihadists have pledged allegiance to the group, increasing jitters in Europe over young, often unstable men being lured by IS propaganda and calls to carry out attacks in their home countries.
IS also claimed that Mohamed Lahouaiej Bouhlel, who killed 84 people when he ploughed a truck into a crowd in the French city of nice on July 14, was one of their "soldiers", however no direct link has been found.
France was still deep in mourning over the massacre when two men stormed into a church in the northern town of Saint-Etienne-du-Rouvray during morning mass on Tuesday and slit the 86-year-old priest's throat at the altar before being gunned down by police.
Another man was left seriously injured in a hostage drama, while three nuns and a worshipper escaped unharmed.
One of the attackers was identified as French jihadist Adel Kermiche, 19, who was awaiting trial on terror charges and had been fitted with an electronic tag despite calls from the prosecutor for him not to be released.
Sources close to the investigation said they found an identity card belonging to one Abdel Malik P, also 19, at Kermiche's home, who they believe is the second attacker.
They said Abdel Malik "strongly resembles" a man hunted by anti-terrorism police in the days before the attack over fears he was about to carry out an act of terror.
In a video posted on the IS news agency Amaq, two bearded men, calling themselves by the noms de guerre Abu Omar and Abu Jalil al-Hanafi, hold hands as they swear "obedience" to IS leader Abu Bakr al-Baghdadi.
President Francois Hollande, members of his government and opposition rivals gathered together at the symbolic Notre-Dame cathedral in Paris for a mass attended by Muslim, Jewish and Christian leaders to pay tribute to the murdered priest.
The moving gathering provided a rare show of unity and respite from days of political sniping over the repeat attacks, which right-wing parties say are due to the Socialist government's failure to protect citizens.
"Those who drape themselves in the finery of religion to hide their deadly project, those who tell us of a God of death, a Moloch (false god) who rejoices in the death of man and promises heaven to those that kill by invoking him. They cannot hope that man gives in to their illusion," said Cardinal Andre Vingt-Trois at the service.
The mass came after a meeting earlier in the day between Hollande and top religious leaders who warned French people against being drawn in by IS efforts to pit different believers against each other.