Lazar did not name the man or say when he was in Hungary, nor whether those he picked up went on to take part in the November 13 atrocities in the French capital claimed by the Islamic State group.
Speaking to AFP on condition of anonymity, a government source later confirmed that the man was in fact Abdeslam, a key suspect in the Paris attacks who is currently on the run.
Lazar meanwhile said the suspect had been in Keleti station in Budapest, "recruiting a team from immigrants who had refused to register with Hungarian authorities", referring to migrants.
He then "left the country together with them," Lazar added.
Until mid-September, when Hungary sealed its border with Serbia, thousands of migrants and refugees spent days or even weeks in makeshift camps at Keleti station on their way to northern Europe after travelling up through the Balkans.
A French source familiar with the investigation told AFP that a car rented by Abdeslam is known to have been in Hungary on September 17.
It was unclear however, whether Belgian-born Abdeslam -- who played a key role in the Paris attacks in which 130 people were killed -- was himself in the vehicle, and if so, whether he was accompanied, the source added.
Abdeslam, 26, was also registered as having been in Austria on September 9 after being stopped in a routine traffic check, Austrian authorities said on November 17.
He and two other men were stopped in a car with Belgian number plates after travelling south from Germany, not west from Hungary.
Abdeslam told police he was "on holiday".
Austrian authorities last month said that the two others "have so far not been named in connection" with the Paris attacks.
Abdeslam, whose brother Brahim blew himself up in a bar the night of the attacks, was spirited away from Paris to Belgium after the November 13 massacre by two other men who were later arrested and charged there.
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