The Iraqi government called on armed groups to follow the lead of the biggest Shiite militia and freeze their operations, while the U.S. military on Friday reported the deaths of two more American service members in fighting against Sunni insurgents.

A statement by Prime Minister Nouri al-Maliki's office welcomed Wednesday's decision by anti-American cleric Muqtada al-Sadr to freeze attacks by his Mahdi militia for up to six months as a step toward "affirming security and stability."

The statement, issued late Thursday, said al-Sadr's move offered "a good chance" to "suspend the work of other militias" to restore "the integrity and sovereignty of Iraq."

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Al-Sadr issued the order after his fighters were suspected of a role in this week's gunfights during a religious festival in Karbala that killed up to 51 people.

A shadowy faction of the Mahdi Army — the Free Men's Brigade — rejected al-Sadr's order, noting that the young cleric had said in the past that only the country's Shiite religious leadership could halt the militia's operations.

Little is known of the faction, which emerged this month in southern Iraq. Al-Sadr loyalists in Baghdad suspect its ranks include mostly Shiites who were Saddam Hussein supporters.

Al-Sadr's order appeared to have had a calming effect in Baghdad, where police on Thursday found only five bodies of bullet-riddled victims of sectarian death squads.

In Sadr City, the Shiite slum in northeast Baghdad, residents said there was no sign of Mahdi militiamen, who normally cruise the streets in cars and converge on al-Sadr's office in the evening.

The Mahdi Army has been accused by Sunni Arab politicians of massacring thousands of Sunni Arabs. The U.S. military believes Iranian-backed splinter groups from the organization have been responsible for most of the recent attacks in the Baghdad area that have caused American casualties.

Mahdi militiamen have been locked in a bitter struggle with other armed Shiite groups for supremacy in the Shiite southern heartland of southern Iraq, which includes major religious shrines and the bulk of the country's vast oil wealth.

The two U.S. service members — a Marine and an Army soldier — were killed Wednesday in fighting in Anbar province, the Sunni Arab stronghold west of Baghdad, the military said.

That brings the total U.S. troop deaths in Iraq to at least 79 this month, one more than the July total, which was the lowest monthly figure this year.

The U.S. statement gave no further details.

However, the military said Marines from the 5th Regimental Combat Team killed 12 suspected Al Qaeda in Iraq fighters and destroyed two vehicles in fighting Wednesday near the Anbar city of Fallujah.

Marine AV-8B Harrier jets dropped two precision-guided bombs, and Marines also called in artillery strikes against the insurgents during the battle, the military said.

"Numerous weapons and roadside bomb making materials were also found," the U.S. statement said.

U.S. officials have reported a dramatic drop in violence in Anbar after numerous Sunni Arab community leaders broke with Al Qaeda in Iraq last year. Some members of other insurgent groups have joined forces with the U.S. to hunt down Al Qaeda members.

The apparent turnaround in Anbar is expected to figure prominently in September reports to Congress, where prominent Democrats and Republicans have called for a drawdown in U.S. forces here.

The reports, including one by the top U.S. commander Gen. David Petraeus, are expected to point to some limited success in curbing violence but little progress toward political power-sharing agreements among Shiites, Sunnis and Kurds.

On Friday, al-Maliki said political leaders were close to finalizing a draft law providing for provincial elections, one of the 18 benchmarks set down by Congress.

At a news conference Thursday, Foreign Minister Hoshyar Zebari insisted that Iraq has been making some headway in resolving political differences, despite defections by the main Sunni Arab bloc and a hard-line Shiite faction.

"The whole world is waiting anxiously to see what this report will indicate," Zebari said. "I personally believe that this report would not provide any magical solutions or provide any instant answers to the difficulties and challenges we are going through."

Complete coverage is available in FOXNews.com's Iraq Center.