Ejehi said a final report on the cause of Beheshti's death may take as long as 45 days to release. He said copy of a letter of complaint in Beheshti's name against his interrogator was found.
The semiofficial ISNA news agency quoted Ejehi as saying that Beheshti charged in the letter that he was subject to "threats, insults and beatings."
Ejehi said Iran's judiciary chief, Ayatollah Sadeq Larijani, has ordered a full inquiry into the death.
The government-owned Iran Network news website said three interrogators involved in the case have been arrested. The website, inn.ir, did not provide further details.
The Tehran police chief, Gen. Hossein Sajedinia, also confirmed that Beheshti died while in cyber police custody.
"The deceased had been handed over to cyber police for completion of investigation under a judicial order for a period of time," Sajedinia told Asr-e-Iran news website Monday.
The 35-year-old Beheshti was said to be a factory worker. He was not a well-known activist.
Dozens of bloggers and journalists have been arrested in widespread crackdowns in Iran in recent years.
In 2010, Iran's parliament played a major role in probing the deaths in detention of three people during the unrest that followed the disputed 2009 presidential elections. The inquiry led to the dismissal of several judicial and police officials.
- AP