Iran's June presidential vote plunged the country to its biggest domestic political crisis in three decades and exposed deep divisions among its ruling elite.
While a security crackdown has largely stopped the big street protests that followed the vote, opposition leaders have remained vocally critical of the government and authorities.
"I suggest a referendum for a way out of the crisis and to end the governing of the Guardian Council," Karoubi said, according to opposition Jaras website, referring to the country's top legislative watchdog.
Opposition leaders Mirhossein Mousavi and Karoubi have said the vote was rigged to secure the re-election of hardline President Mahmoud Ahmadinejad. The authorities deny the charge, saying it was the "healthiest" election the country has had.
The Guardian Council is a 12-man body, six senior clerics appointed by the Supreme Leader and six Islamic jurists, which must ensure all laws agree with Islamic Sharia law and Iran's constitution.
It is also in charge of vetting candidates for presidential and parliament elections.
Karoubi also criticized the heavy presence of "police and security forces" on February 11 when Iranians held rallies throughout the country to mark the 31st anniversary of the Islamic revolution.
"They (police) strongly confronted anyone who showed the smallest sign of disapproving the current situation," Karoubi said in his statement.
Thousands of people were arrested after the June vote. More than 80 people, including senior reformist figures, have received jail terms of up to 15 years.
Last month, Iran hanged two people sentenced to death in post-vote trials. The West and human rights groups condemned the executions, accusing Iran of holding "show trials."
(Editing by Jon Hemming)
