An Iraqi army soldier mans a machine gun atop an armored vehicle Friday at a checkpoint in central Baghdad, Iraq. U.S. and Iraqi forces pushed deeper into Sunni militant strongholds in Baghdad, where cars rigged with explosives greeted their advance.

Baghdad, Iraq ? As a military offensive seeks to bring Baghdad from the brink of anarchy, a top Iraqi security officer tried Friday to measure its early stages using the grim logic of a place with daily bloodshed: by counting the bodies arriving at the morgue.

A total of 10 corpses were collected off the streets – apparently all victims of the city’s lawless jumble of gang justice and sectarian payback. The daily body tally recently has often been 40 or more, excluding major bombings, said Brig. Gen. Qassim Moussawi.

This was the basis for an upbeat message by Moussawi, a spokesman for the joint U.S.-Iraqi security sweep that began this week and has so far faced limited resistance. But his American counterparts remain much more guarded.

“I would say that it is way too early to establish any trends,” said Lt. Col. Chris Garver, a U.S. military spokesman. “We’ve just started to focus our operations. We have months to go to see if we are going to succeed or not.”

Maj. Gen. Joseph Fil, commander of U.S. forces in Baghdad, attributed the reduction in violence not only to the increased security presence but also to an apparent decision by the militias and insurgents to lay low for a while.

“But make no mistake, we do not believe … that’s going to continue, and we do expect there are going to be some very rough, difficult days ahead,” Fil said. “And this enemy knows how – they understand lethality and they have a thirst for blood like I have never seen anywhere before.”

The contrasting outlooks cut across the entire mission, dubbed Operation Law and Order, which seeks to reclaim the streets. Powerful militias and freelance vigilantes have carved Baghdad into fiefdoms and made even daily errands a gamble that could end with a car bombing or gunfire.

The Iraqis are eager to show clear progress to boost the leadership of Prime Minister Nouri al-Maliki. U.S. commanders, however, are approaching the neighbor-by-neighbor sweep as a methodical campaign without quick victories – learning from past mistakes of pouring through an area, only to find that militiamen simply went underground and returned after American forces left.

“We are just at the beginning stages,” Garver reminded.

But evidence of the offensive against militants appeared around the country.

Borders to Iran and Syria have been temporarily sealed in attempts to foil suspected supply routes. In Diyala province northeast of Baghdad, U.S. forces are under sharply escalating attacks from Sunni Muslim insurgents – suggesting that some groups have shifted from Baghdad to other areas to sidestep the crackdown in the capital.

U.S. military officials said demolition experts destroyed a bomb-making factory they linked to the al-Qaida in Iraq faction in Salman Pak, just southwest of Baghdad. The statement said the workshop contained about 1,000 pounds of explosives.