His accusation lent support to fellow reformist leader Mehdi Karoubi, who has come under fire from hardliners for saying some post-election protesters were raped in jail. The authorities have rejected the accusations as "baseless".
"They (authorities) asked those who were abused and raped in prisons, to present four witnesses (to prove their claim)... Those who committed the crimes were the establishments' agents," Mousavi said in a letter to Karoubi, the reformist mowjcamp.com website reported.
"They were threatening detainees to keep silent ... it is not possible to appease the suppressed people by using money and force," Mousavi said.
Some hardliners have called for Karoubi to be arrested or tried if he failed to prove the abuse accusations. Karoubi says he has evidence of mistreatment of detainees. Last Thursday, he said some of those arrested were killed under torture.
"I praise your courage and hope the other clerics join and strengthen your efforts," Mousavi's letter said.
"It is the main duty of revolutionary clergy to reflect the realities, but some have closed their eyes and ignored this responsibility," it added.
Iran arrested thousands of people after the election during its worst street unrest since the Islamic revolution three decades ago.
At least 200 people remain in jail, including senior moderate politicians, activists, lawyers and journalists. Iran has this month staged three mass trials against detainees.
