Adel Kermiche, 19, was wearing an "electronic tag" during the deadly hostage incident at a Catholic church in the town of Saint-Etienne-du-Rouvray, prosecutor Francois Molins said.
The monitoring apparatus was a condition of his house arrest after two attempts in 2015 to travel abroad -- at least once to Syria -- using a relative's identification, Molins said.
Kermiche was identified via fingerprints after the attack, which French President Francois Hollande said was committed in the name of ISIS.
The second killed attacker has not been identified.
Speaking to journalists in the town where the two men took five people hostage during morning Mass on Tuesday, Hollande said the attack was a "cowardly assassination" carried out "by two terrorists in the name of Daesh" -- another name for ISIS.
The Rev. Jacques Hamel, 86, was stabbed in the chest and had his throat slit, Molins said.
The incident comes at a time when France is still grieving a Bastille Day terror attack that left 84 dead amid efforts to contain radicalized Muslims within its borders.
Hollande urged the public to remain unified in the face of the threat.
"All people feel affected so we must have cohesion. ... No one can divide us," he said. "Terrorists will not give up on anything until we stop them."
A witness said congregants pleaded with the attackers to stop.
Besides the slain priest, three nuns and two churchgoers were taken hostage, Molins said.
Another victim, who was not identified, was stabbed in the hip and throat, Molins said. The person is in stable condition, he said.
Sister Daniele Delafosse said she was able to escape the attack, according to CNN French affiliate BFMTV.
Before she fled, she witnessed the perpetrators gather around the church altar and perform some sort of religious oration in Arabic before forcing Hamel to his knees and placing a knife to his neck, she told the station.
Police attempted to negotiate through a small side door in the church, but they could not enter the building sooner because of the hostage situation, Molins said.
One of the killers wore a fake explosive belt, and the other carried a kitchen timer and fake bomb, he said. They were captured as they exited the church.
One of them shouted, "Allahu Akbar" -- Arabic for "God is the greatest" -- as they left the church.
Trouble keeping track
France has been under a state of emergency since the Paris terror attacks in November last year, and French authorities have struggled to monitor thousands of domestic Islamic radicals on their radar.
In response to the heightened terror threat, Hollande has vowed to double the number of officials charged with the task.
The priest's killing follows a string of violent attacks across Europe in recent days, some claimed by the Sunni terror group ISIS, including the Bastille Day attack in Nice
According to a French intelligence source, Kermiche tried to enter Syria twice after becoming radicalized following the Charlie Hebdo magazine office attacks
in Paris. The attacker was associated with Maxime Hauchard, a French jihadi who appeared in an ISIS beheading video in 2014, the source said.
Molins confirmed that Kermiche tried to leave the country twice for Syria in 2015.
He was placed under "judicial control" in March 2015 after trying to use his brother's identification to go to Syria last year. Two months later he left the country for Syria using a cousin's identification card.
He was stopped in Turkey by authorities there, and deported to France via Switzerland, from where he had entered Turkey.
He was detained until March 18, 2016, when he was released under house arrest with an electronic monitoring tag. An appeals court upheld the terms of his release, which required him to live with his family under house arrest and sign in once a week at the local police station.
The ISIS-linked Amaq News Agency released a statement Tuesday, posted by the group's supporters, claiming the Normandy attackers were the terror outfit's "soldiers." The statement uses language similar to the wording that Amaq recently adopted following the Nice, France, attacks, the southern Germany stabbings and the suicide attack on the German music festival.
CNN cannot independently confirm the claim, and no evidence has surfaced showing ISIS had been in direct contact with the attackers.
Hollande has called off a scheduled trip to Prague, Czech Republic, on Wednesday and will instead hold meetings in France with religious leaders, defense officials and other government ministers, the Élysée Palace said.
Speaking to reporters, Hollande said: "Daesh has declared war on us. We have to win that war."
Vatican condemns killing
The Vatican condemned the attack, calling it particularly horrific as it had taken place in a church, "a sacred place where the love of God is announced," according to a statement.
The Pope had been informed of the attack and shared the pain and horror in response to the "absurd violence."
Archbishop Dominique Lebrun of Rouen called on the faithful "to lower their arms before violence and to become an apostle of a civilization of love."
The "Catholic church cannot take up any other weapons but prayer and brotherhood among men," he said in a statement.
Other religious leaders were quick to condemn the violence.
"Evil attacks the weakest, denies truth (and) love, is defeated through Jesus Christ. Pray for France, for victims, for their communities," the Archbishop of Canterbury, Justin Welby, said in a tweet.
Pope Francis and Hollande spoke after the attack, the presidential palace said. The President told the pontiff that "everything would be done to protect its churches and places of worship," according to a statement from Hollande's office.
French Prime Minister Manuel Valls expressed horror at the "barbaric attack" on the church, and vowed a defiant response.
"We will stand together," he said on Twitter.