Officials with the Shiite United Iraqi Alliance said preliminary results showing them with a clear lead in the Dec. 15 elections reflected the will of the people. They countered claims of irregularities by charging that many violations took place in Sunni Arab areas.
They added, however, that they had begun talks with other groups about the possibility of forming a "national unity government."
At least one Sunni Arab leader said he was upset by the Shiite comments.
Meanwhile, at least eight people were killed by gunmen around Baghdad. Gunmen on Friday also tried to assassinate a judge on the Supreme Iraqi Criminal Court that is investigating Saddam Hussein and members of his regime, a court spokesman said Saturday.
The disagreements between the various sectarian and political groups that participated in the elections illustrate the difficulties that lie ahead as Iraq tries to forge its first four-year government following the fall of Saddam.
"There is no doubt that these elections were impartial and reflected the will of the Iraqi people and that their results must be respected," said Hussain al-Shahristani, a senior Alliance official and deputy speaker in the current parliament.
The comments came one day after thousands of people demonstrated in Baghdad and elsewhere claiming election fraud. They demanded that elections be held again in Baghdad and other areas where they allege irregularities took place.
"The door is open for dialogue with our brothers and partners because we believe that Iraq cannot stand up without its main components. Dialogue has already started away from these voices that we hear on the streets," said another senior Alliance official, Jawad al-Maliki.
"Dialogue has started between us and between the slates that won in the elections. Our goal is to form a broad-based national unity government."
But he also said that "some of those who have been shocked by their defeat and by the great results realized by the winning slates insist on making trouble." He added that "the results must be accepted and the will of the people must be respected."
Al-Maliki then upped the rhetoric and claimed the street protests were led by former members of Saddam's Baath party and Islamic extremists, and he described reports that militants helped guard some polling stations in Sunni areas as proof of fraud.
"They have stated that what they call 'resistance' has protected the ballot boxes in their areas. This is a confession that rigging has happened. The terrorists cannot play a positive role while they're shedding the blood of Iraqis and rejecting the political process," he said.
Sunni Arab politician Saleh al-Mutlaq said the Shiites "should not accuse us of terrorism. It is not fair that each protester be considered as a terrorist, and anyone who supports the legitimate resistance will be considered a terrorist."
"I heard what they said on television and I feel regret, this is an evidence that we are still behind civilized nations," he told pan-Arab al-Arabyia television.
Many people outside the governing Shiite religious-oriented political bloc, the United Iraqi Alliance, allege the last week's elections were unfair to Sunni Arabs and secular Shiite groups.
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 has rejected an outside review.
The demand was issued after preliminary returns indicated the United Iraqi Alliance was getting a commanding lead in the polls.
About 1,500 complaints have been lodged about the elections, including at least 25 the Iraqi election commission said could be 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.
Washington hopes broader political participation will weaken support among Sunni Arabs for the Sunni-dominated insurgency, which would strengthen security and allow U.S. troops to begin leaving.
Defense Secretary Donald H. Rumsfeld said President Bush had authorized new cuts below the 138,000-soldier level that has prevailed for most of this year. The top military commander in Iraq and the U.S. ambassador have said the reduction would involve two combat brigades, or about 7,000 soldiers.
In violence Saturday:
— Two security guards for Iraq's justice minister were killed in Baghdad's southern Dora neighborhood when gunmen opened fire on a three-cars convoy.
— Unidentified gunmen fired on two police officers in civilian clothes as they were driving through southwest Baghdad. One was killed the other wounded, police said.
— Police found the bullet-riddled bodies of three men in eastern Baghdad.
— Police said unidentified gunmen opened fire on a bakery in Baghdad's southern Saydiya district, killing an employee.
— Unidentified gunmen killed two brothers who owned an appliance store in Baghdad's Mansour district.