The wife of a police employee who killed four colleagues at the Paris force's HQ says he had a psychotic episode, was incoherent and heard voices the night before, reports say.
Mickaël Harpon, 45, was shot dead by police at the scene.
His wife, who is in police custody but not charged, told police that he had a disagreement with his bosses, according to French media.
French officials are trying to establish a motive for the killings.
Police union officials have also suggested that Harpon may have been involved in a workplace dispute.
Speaking at a press conference on Thursday, Paris police chief Didier Lallement said officers had not ruled out any theory about the attack.
He added that the young official who had shot Harpon had only been working at the HQ for six days.
The killings came a day after police went on strike across France over increasing violence towards officers.
A minute's silence was held by police HQ in Paris on Friday in memory of the four staff members who died.
Rassemblés pour un moment de recueillement et d'émotion intense, en présence du Ministre de l'Intérieur, du Secrétaire d’État et du préfet de Police, les agents de la préfecture de Police ont observé une minute de silence en mémoire des 4 fonctionnaires décédés. pic.twitter.com/v8XS7N1Gpf— Préfecture de Police (@prefpolice) October 4, 2019
Police shared a photo of the gathering on Twitter, calling it a "moment of contemplation" that was "deeply moving".
At about 13:00 local time (11:00 GMT; 12:00 BST), the attacker is said to have gone into the building and straight to his office where he began attacking colleagues with a kitchen knife.
He stabbed three people inside two offices and two women on a stairway, before he was shot dead by an officer inside the building's courtyard.
Three men and one woman were killed, Paris prosecutor Rémy Heitz told reporters.
A fifth person was critically injured in the attack, and was sent for surgery. The building is near major tourist sites including Notre-Dame cathedral.
"Police were running around in panic," a witness who was inside the courtyard at the time of the attack told Le Parisien newspaper.
"I was surprised to hear shooting because this is not a place where you hear that kind of thing. I first thought it was a suicide because there are a lot of those at the moment," he added.
Who was the attacker?
According to Interior Minister Christophe Castaner, Harpon was a 45-year-old IT specialist who had worked for the Paris police force for 16 years.
Officials said he had been working in the force's intelligence division.
Mr Castaner said there had been no warning signs about the attacker, adding: "On the face of it, he looked a model employee."
Harpon also had a hearing and a speech disability.
He converted to Islam 18 months ago, according to reports, and had recently stopped talking to female colleagues in the office. But a government spokeswoman has said there is no indication he had been radicalised before the attack.
Police have searched his home in the north of the city and found no evidence that he was radicalised.
Computer equipment seized from Harpon's home is now being examined, French media report.
There were tensions between the knifeman and his supervisor, according to police union official Christophe Crépin.
"I do not think this is a terrorist act," Mr Crépin, who knew the attacker, told Franceinfo Radio.
Police union leader Jean-Marc Bailleul described it as a criminal act, telling BFMTV: "It was a moment of madness."
The attack follows a rare nationwide police strike on Wednesday, which saw thousands of officers demonstrating in Paris over working hours, shortages in resources and controversial pension reforms.
Police unions say there have been more than 50 suicides by police officers since the start of the year.
They blame the rising numbers on difficult working conditions and increasing violence towards police.