Mickael Harpon had contact with members of the Salafist movement, the BBC reported on Sunday quoting prosecutor Jean-Francois Ricard.
He had exchanged text messages of a religious nature with his wife before Thursday's attack, the prosecutor said.
He also defended the deadly 2015 attack on the magazine Charlie Hebdo and other atrocities, Ricard said.
Anti-terror investigators took over the inquiry on Friday (October 4). It was initially regarded as a criminal matter.
The 45-year-old IT expert, who worked at the police headquarters, was shot dead on
Thursday by a junior police officer after he attacked colleagues in several offices at the central police building.
Harpon had converted to Islam and had been in contact with the Salafist movement, Ricard said, in reference to the ultra-conservative Islamic ideology.
The attacker "agreed with certain atrocities committed in the name of that religion", he said.
Among them was the Charlie Hebdo attack in 2015, when Islamist gunmen killed 11 people in the Paris office of the satirical magazine, before shooting dead a policeman outside.
The prosecutor also noted that the killer had changed his style of clothing in recent months and had cut off contact with women.
Police earlier seized computer equipment during a search of the attacker's home in the north of the city.
His wife on Friday reportedly told police that he had been incoherent and had heard voices the night before the attack.
The employee entered the building around lunchtime on Thursday, and proceeded to attack his 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. A fifth person was seriously injured.
The police building is near major tourist sites including Notre-Dame cathedral.
( With inputs from IANS )