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.
French President Francois Hollande has addressed the nation in the wake of an attack on a church in the country's north, in which a priest was killed and another person seriously injured.
Mr Hollande has also cancelled a trip to Prague to discuss European Union affairs following the attack which has been claimed by Islamic State.
He says the country is at war, fighting radicalisation.
(through translation) "This war will be long. The target is our democracy and it will be our shield. It is our unity that makes our strenght. French people, let us be united and that is how we will win against fanaticism because I can assure you that this war we will win. Long live the Republic. Long live France."
