The week-long clashes have continued after security forces fired to disperse protesters, who were trying to storm the provincial government building using rocks and Molotov cocktails.
Iraq's Prime Minister Mustafa al Kadhimi's move was praised by the United Nations. The country's parliament must still ratify the election date.
Mustafa al Kadhimi was nominated by President Barham Salih, state television reported, shortly after the previous designated prime minister, Adnan al Zurfi, announced he was withdrawing after having failed to secure support to pass a government.
At least three rockets hit the US embassy in Baghdad's heavily fortified Green Zone. Although no group claimed responsibility so far, fingers are pointed at Iran-backed armed groups.
The new law changes each of the country's 18 provinces into several electoral districts, with one legislator elected per 100,000 people.
Security forces say none of the demonstrators were taken into custody, while pro-Iran armed groups blamed by protesters for Friday's killings swore they had no role in the violence.
Iraqi authorities reportedly cut off Internet access for nearly all of Baghdad and the southern part of the country on Tuesday as the latest wave of protests resulted in casualties.
Anti-government protesters continue to shut down roads and government offices in the Iraqi capital, escalating a month-long string of rallies demanding political change.
Clashes at anti-government protests kill more than 100 people as protesters and witnesses say security forces and snippers were firing at demonstrators.
Security forces use tear gas, water cannon and live fire to disperse demonstrations over unemployment, corruption and poor public services in capital Baghdad and other provinces.
The Department of State ordered the pullout of employees from both the US Embassy in Baghdad and its consulate in Erbil. Meanwhile, Germany and Netherlands suspended their military missions to Iraq due to regional tensions.
Iraq seeks to forge an independent foreign policy between the American-Iranian rivalry amidst a backdrop of frantic diplomatic visits to Baghdad in recent weeks.
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