There were no immediate reports of casualties from the strikes and no claim of responsibility.
"The enemy ... wants to pit people against each other," says President Ebrahim Raisi, adding the nation has felt "grief and sorrow" over the woman's death in custody.
Seven security personnel were injured as three rockets were fired at Baghdad's Green Zone, where parliament and many government offices and foreign embassies are located.
The headquarters of three ethnic parties of Iranian Kurds have been hit in northern Iraq as Iran's Revolutionary Guard accuses the groups of smuggling weapons into Iran.
Iran's foreign ministry accuses the leaders of the US and some European countries of abusing a tragic incident in support of the "rioters" and ignoring "millions of people" supporting the system.
Soldiers were killed during clashes with PKK terrorist group in Operation Claw-Lock zone in northern Iraq.
Iraq's political deadlock continues as cleric Muqtada al Sadr's key demand to dissolve parliament is rejected by the country's Federal Supreme Court.
Muqtada al Sadr will always have a place and a role to play in the dysfunctional Iraqi status-quo, which helps Iran weild its influence in Iraq.
Two militiamen from cleric Muqtada al Sadr's Saraya al Salam group and another two from Asaib Ahl al Haq paramilitary group were killed in tit-for-tat attacks.
Sadr has been an indispensable political player since the US invasion of Iraq. Experts say he was in a dilemma about whether to be a cleric or a politician.
President Barham Saleh says early legislative elections would be in line with the aspirations of the Iraqi people and would guarantee political and social stability.
Shia cleric Muqtada al Sadr gave his followers "60 minutes" to disperse from Baghdad's streets following two days of deadly clashes between protesters and security forces.
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