Regeni, a 28-year-old Cambridge University PhD student, disappeared on January 25 in central Cairo.
His body was later found by the side of a road bearing signs of brutal torture.
Egypt has denied that its security forces were involved, but Italy recalled its ambassador to Cairo in April in protest at what it said was a lack of progress in the investigation.
The state prosecutor met his counterpart in Rome this week to further the investigation.
"The Egyptian state prosecutor pointed to information that the head of the street vendor union passed on specific information about the Italian student to Cairo police," the statement said.
"Police probed his activities for three days that concluded that his activities were of no concern to national security, and based on that dropped the investigation."
This is the first official Egyptian acknowledgement that Regeni had been on the radar of security services.
Police officials had at first suggested Regeni might have died in a road accident, and have since offered little information on their investigation.
An Italian autopsy showed that his body was covered with cuts and his bones were broken, indicating he was hit with "fists, batons and hammers".
A letter "X" was carved on his forehead and hand, according to the report cited by Italian media.
His parents, Paola and Claudio Regeni, said the report suggested he had been tortured by a "professional".
In March, police linked a gang that it said extorted foreigners to Regeni's death, saying his belongings had been found in the home of the gang leader's wife.
He and four others were killed in a shootout with police.
Today's statement said Egypt's prosecution service was still investigating the gang's links to Regeni's abduction.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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