Marines and Afghan troops used metal detectors and sniffer dogs, searching compound to compound for explosives rigged to explode. Blasts from controlled detonations could be heard about every 10 minutes north of Marjah.
Afghan and international troops want to secure the area, set up a local government and rush in development aid in what is seen as the first test of the new U.S. strategy for turning the tide of the 8-year-old war. The civilian deaths were a blow to NATO and the Afghan government's attempts to win the allegiance of Afghans and get them to turn away from the insurgents.
NATO said two rockets from a High Mobility Artillery Rocket System were aimed at insurgents firing on Afghan and NATO forces, but stuck 1,000 feet (300 meters) off their intended target.
"We deeply regret this tragic loss of life," said Gen. Stanley McChrystal, the top commander in Afghanistan. "The current operation in central Helmand is aimed at restoring security and stability to this vital area of Afghanistan. It's regrettable that in the course of our joint efforts, innocent lives were lost."
McChrystal said he had apologized to Afghan President Hamid Karzai for the accident and had suspended the use of the rocket system until the incident can be reviewed.
Karzai issued a statement minutes earlier saying 10 members of the same family died when the rocket hit a house in Marjah. He ordered an investigation into who fired the rocket. Before the offensive began on Saturday, Karzai pleaded with Afghan and foreign military leaders to be "seriously careful for the safety of civilians."
On the first day of the offensive, NATO reported two troop casualties -- an American and a Briton. Afghan officials said at least 27 insurgents have been killed in the operation.
The offensive, called "Moshtarak," or "Together," is the biggest joint operation since the 2001 U.S.-led invasion of Afghanistan, with 15,000 troops involved, including some 7,500 in Marjah itself. Most of the NATO forces taking part are American or British.
Between 400 and 1,000 insurgents -- including more than 100 foreign fighters -- were believed to be holed up in Marjah.
"We're in the majority of the city at this point," said Lt. Josh Diddams, a Marine spokesman. He said the nature of the resistance has changed from the initial assault, with insurgents now holding ground in some neighborhoods.
"We're starting to come across areas where the insurgents have actually taken up defensive positions," he said. "Initially it was more hit and run."
It could take weeks to completely reclaim Marjah, according to Brig. Gen. Larry Nicholson, a top Marine commander in the south.
"That doesn't necessarily mean an intense gun battle, but it probably will be 30 days of clearing," Nicholson said. "I am more than cautiously optimistic that we will get it done before that."
Sniper fire forced Nicholson to duck behind an earthen bank in the northern part of the town where he toured the tip of the Marines' front line held by Lima Company, 3rd Battalion, 6th Marines.
"The fire we just took reflects how I think this will go -- small pockets of sporadic fighting by small groups of very mobile individuals," he said.
He said insurgents riddled the area with explosives. "We thought there would be a lot," he said, "but we are finding even more than expected."
NATO forces uncovered 250 kilograms (550 pounds) of ammonium nitrate and other bomb-making materials while clearing a compound in Marjah, a coalition statement said. They also found a weapons cache in Nad Ali, which lies to the north, that included artillery rounds, pressure plates and blasting caps.
The United Nations said an estimated 900 families had fled the Marjah area and were registered for emergency assistance in the provincial capital of Lashkar Gah, about 20 miles (32 kilometers) away.
At least two shuras, or council meetings, have already been held with local residents -- one in Nad Ali and the other in Marjah itself, NATO said in a statement. Discussions have been "good," and more are planned in coming days as part of a larger strategy to enlist community support for the NATO mission, it said.
In Marjah, most of the Marines said they would have preferred a straight-up gunbattle to the "death at every corner" crawl they faced as they made their way through the town.
"Basically, if you hear the boom, it's good. It means you're still alive after the thing goes off," said Lance Corp. Justin Hennes, 22, of Lakeland, Florida.
Local Marjah residents crept out from hiding after dawn Sunday, some reaching out to Afghan troops partnered with Marine platoons.
"Could you please take the mines out?" Mohammad Kazeem, a local pharmacist, asked the Marines through an interpreter. The entrance to his shop had been completely booby-trapped, without any way for him to re-enter his home, he said.