Tens of thousands of Sunni protesters rallied in five cities against Prime Minister Nouri al-Maliki, a Shiite accused of monopolizing power. Sunnis also complain of official discrimination.
Sunni protester leaders have rejected a recent call by an al-Qaeda-linked group in Iraq to take up arms against the government, but there is concern militants are trying to exploit the discontent.
In the city of Samarra, rally speaker Sheik Mohammed Jumaa sent a warning to the prime minister. "Stop tyranny and oppression," he said. "We want our rights. You will witness what other tyrants have witnessed before you."
In the cities of Fallujah and Ramadi, both in the western Anbar province, demonstrators blocked the main highway to Jordan, performing Friday prayers, the highlight of the religious week, as part of the protests. Anbar province is a former al-Qaida stronghold that saw some of the fiercest fighting against U.S. forces during the Iraq war. Other rallies were held in the cities of Mosul and Tikrit.
Sunni protesters have staged weekly anti-government marches in Iraq since mid-December.
Earlier Friday, suspected Sunni insurgents detonated four car bombs, killing at least 31 people and wounding 71 in the bloodiest day of attacks since mid-January, police and health officials said.
The bombings targeted an outdoor pet market in Baghdad's northern Kazimyah neighborhood and in a vegetable market in the Shiite town of Shomali in Hillah province, south of the Iraqi capital.
Every Friday, Iraqis converge on markets to shop and spend family time during the Muslim weekend. Markets are a frequent target for militants who seek to inflict large numbers of casualties.
In Baghdad, the first car bomb exploded around mid-morning at the entrance to the Kazimyah market, two police officers said. When panicked shoppers tried to flee the area, a second parked car exploded a few meters (yards) away, according to the officers.
At least 17 people were killed and 45 were wounded in the two blasts, police said. All the victims were civilians.
About an hour later, two car bombs exploded simultaneously at the Shomali market, killing at least 14 people and wounding 26, two police officers said.
Health officials confirmed the casualty figures in each attack. All officials spoke on condition of anonymity as they were not authorized to release information.
Violence has dropped in Iraq since the worst sectarian fighting in 2006-2007, but insurgents carry out near-daily attacks on security forces and civilians in an attempt to undermine the Shiite-led government.
The current spike in attacks comes just over two months ahead of Iraq's April 20 provincial election, the first country-wide voting since the withdrawal of U.S. forces more than a year ago.