Many Sunnis boycotted the January 2005 election in which Iraqis chose a parliament and provincial councils. The vote ushered in representational government, but it also gave majority Shiites and minority Kurds the bulk of power, including at the provincial level.
The U.S. hopes new elections, to be held by Oct. 1 according to the measure, would give the Sunnis more political power and thereby weaken the insurgency.
The three-member presidential council, which must sign off on legislation passed by parliament, had rejected the measure on Feb. 27.
The main sticking point focused on whether local officials or the central government currently led by Shiite Prime Minister Nouri al-Maliki will have the right to ask the parliament to fire provincial governors.
Shiite Vice President Adel Abdul-Mahdi had objected to a provision that gave the power to the prime minister.
Abdul-Mahdi is a senior official in the Supreme Iraqi Islamic Council, the country's largest Shiite party. The party wields considerable regional power and the law's rejection had drawn criticism that Abdul-Mahdi was putting his party's interests above the nation's.
Abdul-Mahdi agreed to sign off on the law, according to Nasser al-Ani, a Sunni lawmaker and presidential council spokesman.
"This is a good, positive step to enhance national unity and defuse the political tension," al-Ani told The Associated Press.
The presidential council, which also includes President Jalal Talabani, a Kurd, and Sunni Vice President Tariq al-Hashemi, said that the law will be sent to the Justice Ministry to be published in the official gazette.
The council said, however, that it will work with the parliament and provincial councils to suggest possible amendments, which would have to be ratified by the parliament. No timeframe was set for the discussions.
Parliamentary speaker Mahmoud al-Mashhadani had suggested such a compromise earlier this month.
Besides the controversial provision on the governor, the measure adopted Wednesday outlined the criteria for candidates and the structure of the provincial councils.
It also called on the Iraqi parliament to pass a separate measure governing how the elections themselves will be held.
The difficulty in passing the law underscored the immense challenges involved in efforts to distribute power among Shiites, Sunni Arabs and Kurds five years after the fall of Saddam Hussein.
Such power-sharing agreements are the end goal of last year's buildup of U.S. troops. The hope has been that the declining bloodshed will remove the fear that has paralyzed Iraqi politicians, enabling them to compromise and strike deals across the sectarian divide.
As the war enters its sixth year, the number of attacks has dropped with the addition of some 30,000 extra American troops, a Sunni revolt against al-Qaida in Iraq and a cease-fire by radical Shiite cleric Muqtada al-Sadr's Mahdi Army militia.
But the levels of violence have been slower to decline in northern Iraq as militants have fled security crackdowns in Baghdad and surrounding areas.
A female suicide bomber detonated an explosives vest packed with ball bearings Wednesday near a bus terminal northeast of Baghdad, killing at least three people, police said.
The blast was apparently targeting a police patrol in a commercial area in Balad Ruz, according to a senior police officer. If the attacker's identity is confirmed, it would raise to eight the number of women suicide bombers so far this year.
That has raised concerns that extremists are making greater use of women as suicide bombers because explosive belts are easier to conceal under their traditional flowing Islamic robes and they are often not treated with the same suspicion as men.
Farther north, U.S. troops accidentally killed three Iraqi policemen and wounded another, the military said, the latest in a series of friendly fire incidents.
The Iraqi patrol, which was responding to an unrelated request for assistance, raised suspicion as it sped toward U.S. troops operating in a cordoned-off area, Spc. Megan Burmeister, a U.S. military spokeswoman, said in an e-mailed statement.
Local police officials acknowledged the Iraqis had sent the patrol without informing the Americans.
A suicide car bomb also struck an Iraqi army building in the northwestern city of Mosul, wounding 14 people, police said. And a bomb stuck to a taxi exploded in central Baghdad, killing the driver and wounding a passenger and three pedestrians, police said.
Associated Press writer Qassim Abdul-Zahra contributed to this report.