He accused the government of making more mistakes by resorting to "violence and killings" to quell the protests over the poll outcome, that saw Mahmoud Ahmadinejad, the incumbent president, re-elected for another term.
"Arresting or killing Mousavi, [another opposition leader Mehdi] Karoubi ... will not calm the situation," Mousavi, who lost the election, said in the statement.
Mousavi also demanded that the government "take responsibility for the problems it has created in the country... and recognise people's right to lawful assembly".
"I say openly that until there is an acknowledgement of the existence of a serious crisis in the country, there will be no possibility of resolving the problems and issues."
Baqer Moin, a specialist on Iran based in London, told Al Jazeera that Mousavi was being both defiant and conciliatory in his statement.
"He's saying: 'if you want war then I am man of war, if you want peace then I am man of peace ... I'm ready to negotiate'.," Moin said.
"Having said that he comes with five suggestions saying that if you really want peace in the country you can't go overnight towards the maximum demand of everybody - we have to move gradually towards a destination."
"So in a sense he is coming with some realistic proposals within the constitution to deal with the current crisis," he said.
Also on Friday, Ayatollah Ahmad Jannati, the speaker of Iran's Guardian Council, accused anti-government protesters of "corrupting God's earth". The charge is punishable by death under Islamic law.
Iran has been in political turmoil since the June poll with Mousavi and the rest of the opposition alleging election fraud.
Despite government measures to curb protests, opposition workers have intermittently taken to the streets of the capital Tehran and elsewhere to vent their anger at Ahmadinejad's re-election, often triggering violent clashes between protesters and security forces.
In the latest round of violence during Ashoura commemorations, eight Iranians - including a nephew of Mousavi - were killed. The opposition said they died in police shooting, a charge denied by the authorities.