The U.S. military announced its first casualties of the offensives, with four troops killed by roadside bombs during the fighting and a fifth elsewhere.

The assaults in western Iraq aim to put down al-Qaeda in Iraq and other Sunni-led insurgent groups that have waged a campaign of violence aimed at wrecking a crucial Oct. 15 national vote on a new constitution. The United States has hoped the new charter would bring together the country's fractious communities, but Sunnis sharply oppose it.

Sunni Arab moderates threatened Tuesday to boycott the voting after the Shiite-led parliament passed new rules over the weekend that make it effectively impossible for Sunnis to defeat the charter at the ballot box.

The new rules deepened alienation over the political process among Sunnis, who had decided to participate in the referendum but to vote no — but who now said the Shiites were using their dominance to stack the deck against them. A boycott would undermine the referendum's legitimacy and strike a blow to hopes that political progress would weaken Sunni support for the insurgency.

"Boycotting the referendum is a possible option ... because we believe that participating in the voting might be a useless act," said Saleh al-Mutlaq, a leading Sunni politician.

The United Nations also expressed concern about the new electoral rules, saying they don't meet international standards. U.N. officials have been meeting with Iraqi authorities and are confident that Iraq will ultimately agree to sound electoral rules, spokesman Stephane Dujarric said. (Related story: U.N. urges change in voting rules)

"Ultimately, this will be a sovereign decision by the Iraqis and it's up to the Iraqi National Assembly to decide on the appropriate electoral framework," Dujarric said. "That being said, it is our duty in our role in Iraq to point out when the process does not meet international standards."

In Baghdad, a suicide attacker set off a car bomb at the main entrance to the heavily fortified Green Zone, a district of Iraqi government buildings and the U.S. and British Embassies. The powerful blast killed two policemen.

The attack came on the first day of Ramadan, the holy Islamic month of fasting. al-Qaeda in Iraq called on its followers to step up attacks against U.S. and Iraqi forces and make it a "month of victory for Muslims and a month of defeat for the hypocrites and polytheists."

Previous Ramadans since the invasion and occupation of Iraq two years ago saw a spike in violence in Iraq — especially suicide attacks, in part because some Islamic extremists believe those who die in combat for a holy cause during the period are especially blessed.

In another statement, al-Qaeda in Iraq urged Sunnis to boycott the referendum, saying U.S. authorities would fix the vote. "You know very well that the Americans are going to supervise collecting the voting boxes and counting the votes," it said.

The military launched its latest offensive in a cluster of cities in the Euphrates River valley about 140 miles northwest of Baghdad. Code-named "River Gate," it was the largest U.S. offensive in the troubled Anbar region of western Iraq this year, the military said. It also included hundreds of Iraqi troops, the largest such contingent of any of the offensives this year.

Airstrikes by U.S. warplanes and dozens of helicopters set off explosions that lit up Haqlaniyah, Parwana and Haditha before dawn Tuesday. Barrages of gunfire also were seen in the night sky. Large sections of Haqlaniyah's power were knocked out.

Some of the strikes took out bridges across the Euphrates in the area to prevent militants from escaping over them into the desert, said Lt. Col. Christopher Starling, the operations officer in Regimental Combat Team 2, which is leading the offensive.