Adnan al-Dulaimi, the head of a Sunni Arab bloc, said on Friday: "We will not accept the exclusion of any segment of the Iraqi people unless they themselves don't want to participate."
Al-Dulaimi predicted that religious Shia parties would be unable to form a government, even though they are widely expected to take the most seats.
That would open the door to a coalition of Sunnis, secular Shia and Kurds, the former Islamic studies professor said.
However, his prediction that the Shia would be unable to form a government is by no means a certainty.
Shia are believed to account for about 60% of the country's 27 million people, and turnout for Thursday's polls in the Shia heartland of southern and central Iraq was reportedly high.
Under the newly ratified constitution, the party with the biggest number of seats gets first crack at trying to form a government that can win parliament's endorsement.
That is likely to be the coalition of Shia religious parties that dominate the outgoing interim government.
"We will not accept the exclusion of any segment of the Iraqi people unless they themselves don't want to participate"
head of a Sunni Arab bloc
Still, a government with strong Sunni Arab representation could help defuse the Sunni-dominated revolt and allow the United States and its allies to begin withdrawing troops next year.
On Friday, General George Casey Jr, the top US commander in Iraq, told Pentagon reporters in a video teleconference that he would make recommendations in the next few weeks about troop withdrawals from Iraq.
But he sought to dampen expectation that a successful election alone would end the revolt and predicted that fighters may step up their attacks to demonstrate that they "are still strong and a factor to be reckoned with".
Before Thursday's election, religious Shia politicians said they expected to win up to 120 seats - a loss of 26 seats from their current level.
The Shia and Kurds won a disproportionate number of seats in the January ballot because so many Sunnis boycotted the election. This time, Sunnis turned out in large numbers.
Jawad al-Maliki, a prominent Shia legislator, said there was "no doubt that initial results show that we will be the strong bloc" but that a coalition would probably be required - possibly with some Sunni Arabs.
Another Shia politician, Mouwafak al-Rubaie, said the Shia would try to form an "inclusive" government even if they do not have to.