Mr Karroubi urged Tehran to review his evidence in "a calm atmosphere"
One of Iran's defeated opposition presidential candidates has said some protesters held after June's disputed poll were tortured to death in prison.
The claim by Mehdi Karroubi comes days after he said a number of prisoners, both male and female, had been raped.
Officials deny the rape claims, but admit that abuses have taken place.
The BBC's Jon Leyne says the opposition is using the issue to keep up political pressure without directly questioning Mahmoud Ahmadinejad's poll victory.
In a post on his website on Thursday, Mr Karroubi alleged that a number of detainees had been tortured to death.
"Some young people are beaten to death just for chanting slogans in [post-election] protests," he wrote.
Mr Karroubi called for the formation of an independent committee to review his evidence in "a calm atmosphere".
On Sunday, the defeated presidential candidate claimed that both male and female opposition protesters had been raped in detention, with some suffering serious injuries.
Mr Karroubi said the people who had told him about the allegations of sexual assault held "sensitive positions".
The claim was supported by a number of human rights groups but quickly dismissed as "totally baseless" by the speaker of Iran's parliament, Ali Larijani.
"Based on parliament's investigations, detainees have not been raped or sexually abused in Iran's Kahrizak and Evin prisons," he said.
The condition under which detained protesters have been held has been controversial, with damaging claims forcing authorities to act.
The Supreme Leader, Ayatollah Ali Khamanei, closed the notorious Kahrizak detention centre saying it had failed to "preserve the detainees' rights".
Police officials have admitted that some of those held since June might have been tortured.
Both the Iranian parliament and judiciary have established committees to investigate the post-election unrest and the government's response.
The BBC's Tehran correspondent Jon Leyne says the issue of prison abuse is both a real concern in itself and has also become a way of criticising the government of President Ahmadinejad without directly challenging the legitimacy of his re-election.
On Tuesday, Iran's authorities said 4,000 people had been detained during the mass protests that broke out in the wake of the 12 June presidential poll, which the opposition says was rigged.
The number was much higher than previous figures, although the authorities said 3,700 of them had been released within a few days of arrest.
Opposition leaders say 69 protesters died in the post-election violence - more than double the official figure of about 30 fatalities.
Iran is currently trying more than 100 detainees over their alleged involvement in the protests.
The trials - of leading opposition figures, activists, journalists, lawyers, workers at foreign embassies and two people with foreign nationalities - have been criticised by several foreign powers, opposition groups and human rights campaigners.
But authorities insist their legal proceedings are completely legitimate and conform to international standards of justice.
Official election results awarded incumbent President Mahmoud Ahmadinejad a sweeping victory in the polls.
He is in the process of selecting a cabinet, which will be submitted to parliamentary approval next week.
Foreign media, including the BBC, have been restricted in their coverage of Iran in the wake of the election protests.