French prosecutors opened an investigation into "voluntary manslaughter" on Monday after a Catholic priest was murdered in the western region of Vendée.
"No terrorist motive" appears in the case, Vice-Prosecutor Yannick Le Goater told reporters after the suspect, who handed himself to police, was placed in custody.
The suspect, Emmanuel Abayisenga, was already under investigation for setting a fire to the Cathedral of Nantes where he worked as a volunteer a year ago, Interior Minister Gérald Darmanin said.
He had been placed in detention before being released under judicial supervision.
Darmanin added that the suspect "testified (to gendarmes) that he killed the priest."
The minister expressed "all his support to the Catholics of our country" and said he was headed to the site in Saint-Laurent-sur-Sèvre.
The priest, aged 61, had been hosting the suspect for "several months," a police source said.
"On behalf of the Nation, I pay tribute to Father Olivier Maire," President Emmanuel Macron tweeted after hailing the clergyman's "generosity."
"Protecting those who believe is a priority," Macron added.
Reached by Euronews, the French anti-terror prosecutor's office said the "facts did not seem to be of a terrorist nature."
Several opposition politicians slammed the government's alleged "failure" after the tragedy.
Abayisenga had been refused political asylum in France after living in the country since 2012.
Far-right leader Marine Le Pen tweeted: "So in France, it's possible to be an illegal immigrant, to set fire to the cathedral of Nantes, never to be expelled, and to re-offend by murdering a priest."
Darmanin said the suspect was not deportable while he was still under judicial supervision and accused Le Pen of "arguing without knowing the facts."