UN officials welcomed the reversal, saying it helped restore integrity to the crucial October 15 referendum and urged all Iraqis to participate.
The United Nations, which was supervising the referendum, and US officials had pressed Iraqi leaders to drop the rule change, which would have made it nearly impossible for disaffected Sunnis to defeat the charter.
"We're very happy about the National Assembly's action. We will now have a referendum law that follows international standards. It provides the ground for a fair referendum, and we call on all Iraqis to come forward to use a democratic right to give their opinion," said Michael Schulenburg, deputy head of the UN mission in Iraq.
After parliament's decision, Sunni Arab leaders dropped their threats to boycott the upcoming vote. American and UN officials were eager to avert the boycott because it would have deeply undermined the constitution's credibility and wrecked efforts to bring Sunnis into the political process.
With the reversal, "there will be no need to call the Sunnis to boycott the elections," Saleh al-Mutlaq, a top Sunni Arab politician, said.
Now Sunni Arab leaders were gearing up to try to veto the constitution at the ballot box.
"With this result, the Sunni Arabs will be able to defeat the constitution, if there is honesty and an international supervision on the process," al-Mutlaq said. "I am sure if there is honesty, 95 percent of Sunni Arabs will vote no."
Washington hopes majority approval for the constitution will unite Iraq's disparate factions and erode support for the country's bloody insurgency, paving the way to eventually begin withdrawing foreign troops.
But it wants Sunni Arabs to participate even though they are campaigning to defeat the charter. Many Sunnis oppose the charter and want it rewritten, believing it would divide Iraq and leave Shias in the south and Kurds in the north with virtual autonomy and control over Iraq's oil wealth, while isolating the minority with little power or revenue in central and western areas.
Sunni Arabs, who make up only 20 percent of Iraq's 27 million population, were dominant under Saddam Hussein but lost influence after his ouster. The majority Shias and the Kurds overwhelmingly support the constitution.
Under the restored election rules, Sunnis can defeat the document if they get a two-thirds "no" vote in any three provinces, even if a nationwide majority approves the charter. Sunnis have a chance of doing so in four of 18 provinces.
The Shia-dominated parliament tried to close that loophole Sunday by passing a new interpretation of the rules, determining that a simple majority of those who cast votes was needed to pass the constitution -- but that two-thirds
That effectively raised the bar for defeating the constitution to an impossible level, and the United Nations cried foul. After a brief debate Wednesday, the National Assembly voted 119 to 28 to restore the original voting rules for the referendum. Only about half of the 275-member legislative body turned up for the vote.
The text approved by parliament Wednesday confirmed that the word "voters" throughout the election rules in the interim constitution has a single meaning: those who cast votes.
"The word 'voters' in paragraph (c), article 61 of the Transitional Administrative law, means registered voters who actually cast their votes in the referendum," reads the text, according to deputy speaker Hussain al-Shahristani.
"The government is completely keen to make the constitutional process legitimate and of high credibility and we are concerned about the success of this process rather than the results of the referendum," government spokesman Laith Kubba said after the vote.
Wednesday's vote came after intensive talks by UN and American officials to pressure the Iraqis to reverse the rule change.
The rules passed over the weekend had made the constitution unbeatable. In a province of 1 million registered voters, for example, 660,000 would have to vote "no" -- even if that many didn't even come to the polls.
Sunnis were infuriated, accusing the Shia-led government of fixing the rules to guarantee a victory. The UN said the change was a violation of international standards.
With the original rules restored, officials turned their attention to racing to prepare for the vote, which was only 10 days away. On Monday, UN officials began distributing 5 million copies of the constitution to voters across Iraq.
The UN mission in Iraq said Tuesday it has delivered more than 4.4 million pounds of ballots, polling boxes and voter screens.
Sunni participation, however, is also tied to security in the central provinces where they are concentrated and where the Sunni-led insurgency is at its strongest. The location of polling stations has not been announced in the volatile Anbar province for fear they will be attacked -- although officials promised to flood the media with their locations just before the vote so residents know where to go.
The US military is waging two major offensives in Anbar, one at the Syrian border, the other around the town of Haditha, about 220 km northwest of Baghdad to drive out al-Qaida and Iraqi militants. Commanders are promising to finish the assaults in time for the voting to allow residents to go to the polls.