The marchers, some carrying photos of former interim prime minister Iyad Allawi, the leader of the secular Iraqi National List, demonstrated in Baghdad on Tuesday.
"No Sunnis, no Shias, yes for national unity," marches chanted in favour of a national unity government that would give more power to Sunni Arabs and secular Shia.
"We're protesting to reject the elections fraud. We want to ask the government and the elections commission: 'Where did our votes go? Who stole them?"' said Abdul Hamid Abdul Razza, a 45-year-old barber.
The protest came as three opposition groups warned of a wave of protests and civil disobedience if fraud charges are not properly investigated.
The warning came from Allawi's list and two Sunni Arab groups.
Meanwhile, attacks on security forces continued, with five Iraqi police and two bystanders killed early on Tuesday.
Clashes erupted between armed men and Iraqi police in Baghdad, killing two policemen and two bystanders and wounding five people, Captain Firas Keti said.
Five Iraq policemen and two
bystanders died on Tuesday
South of Baghdad, a roadside bomb targeting a police patrol killed two officers and wounded two, and armed men in southern Baghdad killed one officer and wounded another, police said.
Violence increased across Iraq after a lull following the 15 December parliamentary elections, with at least two dozen people killed in shootings and bombings on Monday mostly targeting the security services.
Preliminary figures, including some returns released on Monday from ballots cast early by expatriate Iraqis and some voters inside Iraq, have given a big lead to the religious Shia bloc that controls the current interim government.
Iraq's Electoral Commission said on Monday that final results for the 275-seat parliament could be released in about a week.
Sunni Arab and secular Shia factions are demanding that an international body review more than 1500 complaints, warning they may boycott the new legislature.
They also want new elections in some provinces, including Baghdad.
"We will resort to peaceful options, including protests, civil disobedience and a boycott of the political process until our demands are met"
Hassan Zaidan al-Lahaibi, member of the Iraqi Front for National Dialogue
The UN has rejected an outside review.
"We will resort to peaceful options, including protests, civil disobedience and a boycott of the political process until our demands are met," Hassan Zaidan al-Lahaibi, of the Sunni-dominated Iraqi Front for National Dialogue, said.
Among the complaints are 35 that the election commission considers serious enough to change some local results.
But Farid Ayar, a commission official, said: "I don't think there is a reason to cancel the entire elections."
He also said preliminary results from early votes by soldiers, hospital patients and prisoners and overseas Iraqis showed a coalition of Kurdish parties and the main Shia religious bloc each taking about a third.
Those nearly 500,000 votes were not expected to alter overall results significantly.
Preliminary results previously released gave the United Iraqi Alliance, the Shia coalition dominating the current government, a big lead, but one unlikely to allow it to govern without forming a coalition with other groups.
Hopes of an end to the violence
after the polls have been belied
Bahaa al-Araji, a member of the Shia alliance, said the group was preparing to negotiate with other political blocs and had already met with the Sunni Arab Iraqi Islamic Party.
Al-Araji also said likely candidates for prime minister were current Prime Minister Ibrahim al-Jaafari, who heads the Islamic Dawa party, and Adel Abdul-Mahdi, who belongs to the other main Shia party, the Supreme Council of the Islamic Revolution in Iraq.