BAGHDAD, Iraq - Following sharp criticism from the international community and Sunni leaders, Iraqi lawmakers voted today to reverse changes they made to rules governing next week's referendum on a new constitution.

The National Assembly overwhelmingly voted to clarify that the passage of the Oct. 15 referendum would depend on actual ballots cast rather than on the total number of registered voters.

The decision, by a 119-28 vote, comes three days after Kurdish and Shiite lawmakers quietly agreed on last-minute changes that would have made it virtually impossible for the charter to fail, infuriating Sunni opponents and prompting the United Nations to press for a reversal of the rules.

"The U.N. said it was not just," said Mahmoud Othman, an independent Kurdish member of the National Assembly. "Today they reversed it."

A spokesman for the United Nations Secretary General's office in New York, Farhan Haq, said today: "We are pleased that they so swiftly took this decision. We had informed them of our concerns about the previous change made on Sunday. It seems that the Iraqi National Assembly was willing to hear our arguments and that they were willing to make the changes necessary to bring the election law back into line with international standards."

"The language that had been used on Sunday created a bit of a contradiction," Mr. Haq said. "That confusion has now been cleared up."

The criticism by the United Nations on Tuesday was especially significant because the organization was brought in to supervise the referendum and confer a stamp of legitimacy on it.

International observers as well as some members of the National Assembly had warned that the rule change would seriously damage the credibility of the vote, a crucial moment in Iraq's transition to full independence. Sunni Arab leaders had threatened to boycott the referendum.

At the center of the dispute was the definition of the term "voters." Under the rules that were passed on Sunday, the constitution would have failed only if two-thirds of all registered voters - rather than two-thirds of those actually casting ballots - had rejected it in at least three of the 18 provinces. Given that less than two-thirds of voters participated in the January legislative elections in Iraq, that would have made it almost impossible for the document to fail.

The fact that elsewhere in the legislation the term "voters" referred to actual ballots cast had prompted accusations of an unfair double standard that violated the intent of the law. "When there is a contradiction on two different interpretations within one text, that would become an issue," Stéphane Dujarric, a spokesman for Secretary General Kofi Annan, said during a news conference at the United Nations in New York on Tuesday. Shiite representatives had said they modified the law because they feared that violence in some provinces could keep people away from the polls and allow a small number of voters to overturn the constitution, even if much larger numbers approve it elsewhere.

Mr. Othman said Shiite and Kurdish representatives had floated a compromise proposal on Tuesday under which the rule change would be canceled. But they added a proviso: rejection of the constitution would be valid only if voter turnout in the three provinces voting against it was equivalent to the average turnout across Iraq.

That kind of turnout is very unlikely, given past instances of violence and voter intimidation in the Sunni-dominated provinces where opposition to the constitution is high, and the United Nations rejected the proposal, Mr. Othman said.

The political struggle unfolded as about 2,500 American and Iraqi troops began a major offensive along the Euphrates River west of Baghdad, in an effort to root out insurgents loyal to Abu Musab al-Zarqawi and prevent them from intimidating voters.

It was the latest attempt by the American command to strike at insurgents who have used the river corridor to smuggle fighters and weapons from the Syrian border to the center of the country.

The sweep, focusing on three river towns, Haditha, Haqlaniya and Barwana, in Anbar Province, follows large-scale operations intended to choke off insurgents' supply routes. Past efforts have secured only limited gains, because insurgents mostly just melted away in the face of the offensives and returned once the troops had left.

Military officials also announced Tuesday that four American soldiers and a marine were killed Monday in three incidents. Three soldiers were killed by a roadside bomb in Haqlaniya while on a mission before the offensive in Anbar, officials said. A marine was killed by a roadside bomb near Qaim, on the Syrian border, where about 1,000 troops have been conducting a separate counter-insurgency sweep.

A fifth American died in a shooting near Taqaddum, close to Falluja, though military officials did not explain the circumstances of the shooting or whether it was combat-related, mistaken fire by friendly troops, or self-inflicted.

American and Iraqi military officials have warned that insurgents are likely to step up their campaign of violence as the vote approaches.

Al Qaeda in Mesopotamia, the terrorist group led by Mr. Zarqawi, is using the holy month of Ramadan, which began Tuesday for most Sunnis and will begin Wednesday for Shiites, to encourage his loyalists to step up their attacks on foreign forces. He called Ramadan "a month of serious work, jihad and initiative."

The latest Anbar offensive came on a day of scattered violence around Iraq, including a gun battle that broke out in southern Baghdad between guerrillas and a combined force of Iraqi and American troops, officials said. More than three dozen insurgents were killed, wounded or captured in the fight, according to the American military.

In another clash, insurgents battled with Iraqi police commandos in Yusifyia, south of Baghdad, killing at least 4 commandos and wounding 12, an Interior Ministry official reported.

In Baghdad, a suicide car bomb exploded at a busy entrance to the heavily fortified Green Zone, killing two Iraqi soldiers and a civilian and wounding seven people, an Interior Ministry official reported. The gate, one of several leading into the zone, had been a target before: in July insurgents carried out a dramatic triple attack there involving a suicide car bomb and two suicide bombers on foot.

Annotazioni − Sabrina Tavernise contributed reporting from Baghdad for this article, Warren Hoge contributed from the United Nations and Katrin Bennhold from New York. An Iraqi employee of The New York Times contributed from Kirkuk.