Kermiche was known to security services, having twice been arrested on his way to Syria, and was under house arrest and wearing an electronic monitoring bracelet at the time of the attack.
Molins said Kermiche and an unknown accomplice, armed with knives, had stormed the church in Saint-Etienne-du-Rouvray, taking hostage the 86-year-old priest, three nuns and two worshippers.
One of the nuns managed to escape and call police, who, upon arrival, tried to negotiate with the hostage-takers through a small door.
Molins said police were unable to launch an assault on the church as three hostages were lined up in front of the door.
Two nuns and one worshipper then exited the church followed by the two attackers, one carrying a handgun, who charged police shouting "Allahu Akbar" (God is greatest)
Both attackers had on them a "fake explosive device covered in aluminium foil".
The priest was found dead with his throat slit, and an 86-year-old worshipper had severe knife wounds, said Molins.
Claimed by IS
The Islamic State group said that two of its "soldiers" stormed a church in northern France and slit an elderly priest's throat on Tuesday, the latest attack in a country shaken to its core by repeated terror strikes.
The hostage drama in the Normandy town of Saint-Etienne-du-Rouvray comes less than two weeks after the truck massacre in the French Riviera city of Nice, which killed 84 people and was also claimed by IS.
Two men armed with knives entered the centuries-old stone St-Etienne church in the working-class town during morning mass.
Sister Danielle, a nun who was in the church at the time, said slain priest Jaques Hamel was wearing his white cloak and was at the foot of the altar when "they forced him to get on his knees and not move".
"He tried to struggle, he tried," she told local radio RMC of the priest aged in his 80s. "He knew what was happening."
She said the men were speaking Arabic and shouting and had "recorded" the attack. She managed to run away and alert the police.
Target 'Crusader coalition'
President Francois Hollande said the men had claimed they were acting on behalf of IS before being shot dead by police.
The IS-linked Amaq news agency, citing a "security source", said the perpetrators were "soldiers of the Islamic State who carried out the attack in response to calls to target countries of the Crusader coalition".
It was the fourth attack claimed by IS in Europe in two weeks, carried out by a mixed bag of assailants more or less inspired by the group from afar, some of whom are reported to have suffered mental illness.
This murky profile is creating a nightmare for security services unable to stop the attacks although Hollande insisted the country's anti-terrorism laws were enough.
The French interior ministry said that of the five people taken hostage at the church, three were released unharmed and another was in a critical condition.
A source close to the investigation said the attackers were armed with knives, an old pistol which did not work, and a "fake package" that appeared as if it contained explosives.
The local imam Mohammed Karabila said he was "stunned by the death of my friend. He was someone who gave his life to others. We are dumbfounded at the mosque."
'All stand together'
Pope Francis voiced his "pain and horror" at the "barbaric killing" of the priest.
"The whole of France and all Catholics are wounded. We will stand together," Prime Minister Manuel Valls wrote on Twitter.
France has been on high alert after three major attacks in 18 months.
Grey clouds hung over the town, near-deserted as stores shut down after the attack. Forensic police were combing the site for clues.
An AFP reporter saw police carrying out two raids and at least one person was taken into custody.
Joanna Torrent, a 22-year-old store employee, was stunned to see terror hit her small working class town of 30,000 people, far from bustling tourist hubs like Paris and Nice.
"I thought it would only be in big cities, that it couldn't reach here," she said.
Valls had warned earlier this week that France will face more attacks as it struggles to deal with extremists returning from jihad in Iraq and Syria and those radicalised at home.
'Threat remains very high'
When Mohamed Lahouaiej Bouhlel ploughed a truck into crowds celebrating Bastille Day in Nice on July 14, a bitter political spat erupted over alleged security failings, with authorities accused of not doing enough to protect people.
Hollande called for "unity" in the country and rejected opposition calls to further harden anti-terrorism legislation.
"Restricting our freedoms will not make the fight against terrorism more effective," he said, adding that changes made to legislation already gave authorities sufficient "capacity to act."
"What the terrorists want is to divide us, separate us, to tear us apart. We must avoid one-upmanship, arguments, conflation, suspicions," he said.
"This war will be long. Our democracy is the target, and it will be our shield. Let us stand together. We will win this war."
One of the two attackers has been identified as Adel K, who tried twice to go to Syria and was charged with criminal association with a terrorist enterprise before being freed with the electronic bracelet.
"I am not surprised, he talked to me about it all the time," a teenager who claimed to know Adel K. told RTL radio.
"He talked about Islam, that he was going to do things like this. He said 'I am going to do a church' two months ago. I didn't believe him, he said a lot of things."
The United States condemned the "horrific terrorist attack", National Security Council spokesman Ned Price said in a statement.
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 air strikes against the jihadist group in Iraq and Syria.
After Nice, France extended a state of emergency for the fourth time since IS attackers struck Paris in November, killing 130 people.
