The revelations are likely to fuel criticism of Chancellor Angela Merkel's open-door policy for refugees, after a spate of sexual assaults blamed on migrants during New Year's Eve festivities in Cologne shocked the country.
The man in the thwarted Paris attack had "travelled across Europe and made (asylum) requests everywhere" and "had a criminal past", de Maiziere told ZDF television.
The attacker was killed by French police on Thursday after he tried to storm the police station in northern Paris, brandishing a meat cleaver and wearing a fake suicide vest. Police found a handwritten note on his body in which he pledged allegiance to the Islamic State group.
The attempted police station assault took place exactly one year since the start of a series of jihadist attacks in Paris, beginning with the murder of 12 people at the Charlie Hebdo satirical magazine on January 7, 2015.
On Saturday, German investigators raided an apartment at a shelter for asylum seekers in the western city of Recklinghausen where they said the police station attacker had lived.
The search did not turn up any evidence of other possible attacks, their statement said, without giving further details.
But French Interior Minister Bernard Cazeneuve cast doubt on the German investigators' claims.
"I cannot confirm this, quite simply because I am not at all sure that it is correct," Cazeneuve told France's iTele, speaking before the German interior minister's comments.
Cazeneuve called on the media to exercise the "greatest care" in reporting the man's identity.
'IS flag and symbol'
German news site Spiegel Online reported that the man had already been classed by German police as potentially dangerous after he posed at the refugee centre with an IS flag, but he disappeared in December.
The head of North Rhine-Westphalia's criminal police service, Uwe Jacob, said the suspect had travelled to Germany in 2013 for the first time from France, where he had lived illegally previously for five years.
He had gone under seven different identities and given at least three nationalities on separate occasions -- Syrian, Moroccan or Georgian, Jacob said, according to national news agency DPA.
"We are not sure who he really was," said Jacob, adding that the man had already been imprisoned on several occasions for offences relating to illegal arms possession, drug trafficking and assault.
The Welt am Sonntag newspaper said the man had drawn a symbol of the IS group on the shelter's wall in Recklinghausen and had filed for asylum using the name Walid Salihi.
But French investigators said Friday the suspect appeared to have been identified by his family and was said to be a Tunisian named Tarek Belgacem.
In Tunisia, a woman who claimed to be the man's mother confirmed that he had been living in Germany but denied he had any links to extremist groups.
She told a Tunisian radio station that her son had rung her to ask her "to send him his birth certificate. He was in Germany."
The link to the refugee shelter in Germany, and the apparent ease with which the subject was able to register with the authorities, risks inflaming a debate over the 1.1 million asylum-seekers that the country took in last year.
Mindful of the political sensitivity surrounding the issue, Recklinghausen's mayor Christoph Tesche said it remains "our humanitarian and legal duty to provide shelter for those who flee their homes".
But it was also important to work "intensively with relevant authorities to ensure that people with such intentions cannot hide in our institutions," he stressed.
Tensions are running high in Germany, where more than 500 cases of New Year's Eve violence against women in Cologne have been recorded, with police saying suspects of the crime spree were mostly asylum seekers and migrants.
With anger growing, Merkel has toughened her tone on migrant deportations, declaring that any asylum seekers handed a jail term -- even if it was a suspended sentence -- should be kicked out of the country.
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