There was no suggestion that the policeman were under suspicion in the joint Egyptian-Italian statement.
The statement said prosecutors have also questioned policemen who killed members of a criminal gang in March and claimed to have found Regeni's belongings, including his passport, in the home of the gang leader's wife.
That account met with suspicion in Italy, where politicians and the media have suggested that Egyptian police were behind his death.
The slow pace of the investigation prompted Italy to withdraw its ambassador from Cairo.
Regeni, a 28-year-old Cambridge University PhD student, disappeared on January 25th in central Cairo, as police were out in force in anticipation of protests that day.
His body was later found by the side of a road bearing signs of torture.
He had been researching street vendor trade unions, an especially sensitive political issue in Egypt, with successive governments fearing strikes and unrest.
Egypt has forcefully denied that its police were involved in his abduction. “The Egyptian side said the investigation (into Regeni's murder) included the questioning of policemen who had investigated Giulio Regeni in early January,” the statement said.
“The Egyptian state prosecutor clarified that the police stopped its investigation (of Regeni) when it became clear that his activities did not threaten national security,” it said.
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.