Meanwhile, a lawyer for Saddam Hussein said he saw evidence his client had been beaten.
Several thousand people demonstrated after noon prayers in southern Baghdad, many carrying banners decrying last week's elections.
Many Iraqis outside the religious Shi'ite coalition allege the elections were unfair to smaller Sunni Arab and secular Shi'ite groups.
"We refute the cheating and forgery in the elections," one banner read.
During prayers at Baghdad's Umm al-Qura mosque, the headquarters of the Association of Muslim Scholars, a major Sunni clerical group, Sheikh Mahmoud al-Sumaidaei told followers they were "living a conspiracy built on lies and forgery."
"You have to be ready during these hard times and combat forgeries and lies for the sake of Islam," he said.
Sunni Arab and secular Shi'ite factions yesterday demanded that an international body review election fraud complaints and threatened to boycott the new legislature.
The United Nations rejected the idea.
Criticisms of last week's elections are seen by some as jockeying for position by both Sunnis and former Prime Minister Ayad Allawi, a secular Shi'ite, before negotiations on forming a new coalition government begin. No group is expected to win a majority of the legislature's 275 seats.
The formerly dominant Sunni minority fears being marginalised by the Shi'ite majority, which was oppressed during Saddam's reign.
The demands came two days after preliminary returns indicated that the current governing group, the religious Shi'ite United Iraqi Alliance, was getting bigger-than-expected majorities in Baghdad, which has large numbers of Shiites and Sunnis.
Yesterday, more than 2,000 people demonstrated in Mosul, where some accused Iran of having a hand in election fraud. About 1,000 people demonstrated in Tikrit, Saddam's hometown.
The former leader claimed at his trial this week that he had been beaten by his American captors.
Defence lawyer Khalil al-Dulaimi said he had seen marks on his client's body. Speaking in Amman, Jordan, Mr Dulaimi said he had filed a compliant with the court hearing Saddam's case.
The chief prosecutor, Jaafar al-Mousawi, said he hadn't seen a complaint but planned to visit Saddam and his seven co-defendants to review their health and "listen to their demands and supply them with everything they need."
Meanwhile US Defence Secretary Donald Rumsfeld announced the first of what is likely to be a series of US combat troop drawdowns in Iraq in 2006.
Mr Rumsfeld, addressing US troops in Fallujah a former insurgent stronghold said President George W Bush has authorised new cuts below the 138,000 level that has prevailed for most of this year.
Mr Rumsfeld did not reveal the exact size of the cut, but the Pentagon said the reductions would be about 7,000 troops, about the size of two combat brigades.