"Yesterday (Monday), several people were arrested," Tehran's public prosecutor, Abbas Jafari Dolatabadi, said without elaborating, the ISNA news agency reported.
"When we learned about (Beheshti's) death, we began an inquiry.... We hope to make the findings public within the next 10 days," Dolatabadi said.
The judiciary's High Council of Human Rights said on Sunday that "all aspects of the case have been accurately investigated following a special order by judiciary chief Ayatollah Sadeq Larijani."
Opposition activists say Beheshti, who died on November 3 aged 35, was tortured to death in prison for criticising Iran's regime on the Internet.
The blogger's fate provoked an international outcry, and human rights watchdog Amnesty International said he may have died under torture.
The judiciary says Beheshti was detained in Evin prison, but opposition groups claim he was kept at the notorious Kahrizak detention centre since his arrest in late October at the request of Iran's cyber police.
Kahrizak was temporarily shut down by Iran's supreme leader Ayatollah Ali Khamenei in July 2009 after three inmates died following mistreatment by guards.
Beheshti's death has provoked outrage inside the regime -- a rare case of Iran's acceptance of international criticism over a human rights complaint.
Conservative lawmaker Mohammad Dehqan on Tuesday lambasted the judiciary for failing to prosecute those involved in the Kahrizak fiasco, the Mehr news agency reported.
"We would not have witnessed (Beheshti's death), if guilty agents and judges involved in the Kahrizak incident had been dealt with" by the judiciary, said Dehqan, who sits on the parliament's judicial commission and the residing board.
He also demanded an explanation from the police for its "treatment" of Beheshti, while questioning the force's "previous actions which had tarnished the regime's reputation" and had fuelled what he termed anti-regime propaganda by foreign media.
Hundreds of opposition figures -- politicians, journalists, bloggers, lawyers, rights activists, union figures and media workers -- are in Iranian prisons, according to international human rights groups.