"What we know today is that he is definitely of Tunisian origin, that his name could be Tarek Belgacem and that he had travelled to several countries in the European Union, including Luxembourg, Switzerland and Germany," Cazeneuve told France's iTele.
The minister cast doubt on a statement from the German police yesterday that the man had lived in a centre for asylum seekers in Germany.
"I cannot confirm this, quite simply because I am not at all sure that it is correct," Cazeneuve said, and called on the media to exercise the "greatest care" in reporting on the man's identity.
The man was shot dead by police on Thursday as he tried to storm a police station in the Goutte d'Or district of northern Paris, brandishing a meat cleaver and wearing a fake suicide vest.
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French prosecutors said he was carrying a handwritten claim to be acting in the name of the Islamic State (IS) group.
The assault took place exactly one year to the day after the killing of 12 people at the Charlie Hebdo satirical weekly on January 7, 2015.
The same newspaper reported that he had used different names in separate registrations with German authorities, but filed for asylum using the name Walid Salihi.
But French investigators said Friday the suspect appeared to be a Tunisian named Tarek Belgacem.