Cazeneuve warned that there is still little known about the man, who police have now identified as a Tunisian named Tarek Belgacem. He had stayed in several European countries including Luxembourg, Switzerland and Germany, according to the interior minister.
"As for the information that has been broadcast that he was in a refugee centre in Germany and was seeking asylum, this is information that I cannot confirm because I'm just not sure it is accurate," he added.
German police have told French news agency AFP that the man had been registered as an asylum-seeker and had been living in a refugee centre in the country. They have said that there is no indication that other attacks have been planned.
On Saturday, German investigators assisting the probe into the police-station attack raided an apartment at a shelter for asylum-seekers in Recklinghausen, in the west of the country.
Meanwhile, the German news site Spiegel Online reported that the man had already been classed by German police as a possible suspect after he posed at the refugee centre with an Islamic State group flag, but that he disappeared in December.
Newspaper Welt am Sonntag said the man had drawn a symbol of the Islamic State organisation on the shelter's wall and had used different names in separate registrations with German authorities. He filed for asylum using the name Walid Salihi, according to the newspaper.
The developments are expected to further fuel criticism of Chancellor Angela Merkel's liberal stance towards war refugees and the debate over the 1.1 million asylum-seekers that the country took in last year.
The thwarted attack at the police station was on the one-year anniversary of the deadly attack on the French satirical newspaper Charlie Hebdo.
Paris prosecutor Francois Molins had said the man was carrying a mobile phone with a German SIM card, with French media reporting that it contained several messages in Arabic, some of which were sent from Germany. He also had a hand-drawn picture of the Islamic State group in his clothing.
French police had initially identified him as a 20-year-old Moroccan-born man named Sallah Ali, based on fingerprints from a 2013 arrest on the French Riviera for theft. But the man did not have any documents at the time of his arrest and had told police that he was homeless.