A joint statement issued on Thursday by 35 political groups that competed in last week's elections said the Independent Electoral Commission of Iraq (IECI), which oversaw the ballot, should be disbanded.
It also said the complaints about fraud and intimidation should be reviewed by international organisations such as the United Nations, the European Union, the Organisation of the Islamic Conference or the Arab League.
Reading from a statement, Ali al-Timimi, the head of the secular Shia Hilla al-Fayha List, said: "We hold the IECI responsible for all the violations which took place during the elections and demand that it be dissolved and a suitable alternative to be found.
"If this is not achieved, then we will have no choice but to refuse the results and boycott the new parliament."
A representative for Iyad Allawi, the former prime minister of Iraq, dismissed the voting in all of Iraq's 18 provinces on 15 December as "fraudulent".
Ibrahim al-Janabi also described the elected lawmakers as "illegitimate".
"These elections are fraudulent, they are fraudulent, and the next parliament is illegitimate. We reject all this process," al-Janabi told a news conference.
The groups that signed the joint statement included the main Sunni Arab coalition, Adnan al-Dulaimi's Iraqi Accordance Front, and a secular Shia bloc headed by Allawi.
But a senior member of the Shia religious United Iraqi Alliance, the group leading in the polls following preliminary returns, said the protesters should accept the results.
"These statements will lead the country to new chaos," Ali al-Adib said.
"Who can guarantee that when the elections are rerun they will not reject them again?"
Representatives of different
parties met to contest the results
Al-Adib, who is also a member of the Supreme Council of the Islamic Revolution in Iraq, said the alliance now helping govern Iraq also had complaints.
"We also have complaints and we also have evidence, and we are waiting for the decision of the electoral commission," he said.
"They have to accept the will of the Iraqi people, the will of the majority. The political process will continue even if they boycott it."
He said those rejecting the election results "are the same who called for the boycotting of the last elections and said 'no' to the constitution".
Much of the anger over the results could stem from the Sunni Arabs' losing their dominant political position for the first time in hundreds of years in Baghdad, long the heart of regional Sunni Arab culture and education.
The group dominated politics and government long before Saddam Hussein, himself a Sunni Arab, took control in the 1970s.
The harsh statements also could be part of jockeying for position by both the Sunnis and Allawi for when negotiations begin to form a new coalition government.
It took nearly three months to form an interim government after the elections in January, which gave the Shia 140 seats, the Kurds 75, Allawi 40 and the Sunni Arabs 17.
In another twist, Allawi could be trying to manoeuvre himself into a senior position in a Shia-Sunni coalition.
He did not attend the meeting, held at his headquarters in the heavily fortified Green Zone and attended by more than 100 politicians and representatives of various groups.
The IECI said it had received more than 1500 complaints about violations, 25 of which were serious.
It said it did not expect the complaints to change the overall result, to be announced in January.
"The political process will continue even if they boycott it"
Ali al-Adib, member of the United Iraqi Alliance
Preliminary results show the United Iraqi Alliance winning strong majorities not only in Baghdad but also in the largely Shia southern provinces.
Sunni Arabs turned out in large numbers, unlike in January's election.
The electoral commission put total turnout at 69.97% of the country's 15.5 million voters, compared with 58% in January and 63% in the constitutional referendum on 15 October.
Politicians say the United Iraqi Alliance seems on course to win between 120 and 130 seats, compared with 140 now.
Despite the lead, the Shia religious bloc will probably fall short of the 184 seats necessary to chose a new president, the first step needed to form a government, and will have to find a coalition partner in the 275-member parliament.
Sunni Arabs may increase their seats from 17 to more than 40, while the Kurds are expected to get between 40 and 50.
Allawi, who controls 40 seats, is expected to be the big loser and drop to 20 seats or fewer.