Many people outside the governing Shiite religious-oriented political bloc, the United Iraqi Alliance, allege last week's elections were unfair to Sunni Arab and secular Shiite groups.
"We refuse the cheating and forgery in the elections," read one banner at the protest in southern Baghdad.
More than 2,000 people also demonstrated in Mosul, where some accused Iran of having a hand in election fraud. About 1,000 people demonstrated in Tikrit, Saddam's hometown.
Sunni Arab and secular Shiite factions are demanding that an international body review the fraud complaints, warning that they may boycott the new legislature. The United Nations rejected an outside review.
The demand was issued after preliminary returns indicated the United Iraqi Alliance was getting bigger-than-expected majorities in Baghdad, which has large numbers of secular Shiites and Sunnis.
About 1,500 complaints have been lodged about the elections, including 40 or so that the Iraqi election commission said are serious enough to change the results in certain areas.
The protesting groups have demanded the disbandment of the Independent Electoral Commission of Iraq, accusing it of covering up ballot box stuffing and fraud
