A U.S. Marine breaks the door of a house to search for weapons during an operation in Marjah, Afghanistan, on Tuesday. Reuters

MARJAH, Afghanistan—U.S. Marines and Afghan soldiers seized the site of Marjah's government offices, setting the stage for Kabul to attempt to resume its authority in a town long run by the Taliban.

In a full day of skirmishing, the troops took a former police station in central Marjah, as well as the ruined foundations of the former government center.

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"The government will return to Marjah, and in short order," predicted Lt. Col. Calvin Worth, commander of 1st Battalion, 6th Marine Regiment.

Progress continued to be deliberate—at times slow—in the fourth day of what the U.S.-led coalition bills as its biggest offensive since the Taliban's fall in 2001, and a grand effort to oust insurgent fighters while restoring the credibility of the Afghan government.

On Tuesday, eight more civilians were killed in fighting in southern Afghanistan. Three died in shooting incidents in the assault on Marjah, while five others were killed in the province of Kandahar, where coalition troops erroneously decided that a group of Afghans were planting an explosive device along a trail.

On Tuesday, officials said that human error apparently led to a deadly missile strike on the outskirts of Marjah Sunday, killing 12 people, half of them children.

The first contingent of Afghan National Civil Order Police is expected to arrive in town and report for duty on Wednesday, weeks ahead of what coalition commanders originally envisioned. The force—considered more able and honest than the regular national police—will be the first evidence of Kabul's civil authority.

The U.S. and Afghan troops raised the Afghan flag above the old district center, which is now used as stalls for a weekly bazaar thought to bring the Taliban large of amounts of tax revenue.

Still, the fighting involved suggests that insurgents in southern Marjah are moving north to confront the coalition forces. "We still have a large number of enemy fighters in southern Marjah," Lt. Col. Worth said.

Meanwhile, British Major General Nick Carter, the allied commander of forces in southern Afghanistan, said the phase of Operation Moshtarak, as the massive offensive is known, is at as the "end of the beginning."

Maj. Gen. Carter, a British commander, said Marjah was two-thirds secured and cleared of insurgents. He said it will take "several days" to complete the operation and "days" to clear the area of improvised explosive devices.

"We have had some significant resistance from isolated groups of fighters," he said, adding that allied forces had found foreign fighters in the area, including Pakistan-based insurgents.

Speaking from Afghanistan via a video link, Maj. Gen. Carter said British and Afghan forces had now fully secured what he referred to as the 31 West and 31 East districts in the northeast part of the operating zone. Still, clearing IEDs was "a work in progress and will take some time to conclude," he said.

Further north in town, the arrival of reinforcements allowed the Marines on Tuesday to break the insurgents' stranglehold on an isolated U.S. outpost with relative ease.

Marines from the 1,500-strong 1st Battalion, 6th Marine Regiment, moved methodically through an insurgent warren, picking their way through homemade mines and ending the day in control of about one third of the neighborhood of low homes surrounded by cracked mud-brick walls.

At one point in a nearby bazaar, a lieutenant noticed new wire on an old pole. Further investigation revealed it was connected to eight mortar shells buried beneath 100 yards of road, intended to destroy multiple vehicles in a military convoy. Explosives teams detonated the booby-trap safely.

Just a day earlier, the area, called the Pork Chop for its shape on the map, had been a haven for insurgents, who used positions there to pepper the Marine outpost with sniper fire and rocket-propelled grenades. Since the offensive began on Saturday, insurgents had been moving each morning to fighting positions in the Pork Chop.

On Tuesday, it appeared that the large number of coalition troops and vehicles with heavy weapons prevented the insurgents from making their way there.

The Marine outpost abutting the Pork Chop and a neighboring bazaar, which had been virtually besieged on Monday, was peaceful the following day.

At day's end, the Marines fortified a new front line in the Pork Chop, to avoid risking mine injuries after dark. "I don't want to get into a situation I can't finish tonight," said Capt. Ryan Sparks, commander of the battalion's Company B.

—Alistair MacDonald in London and Alan Cullison in Kandahar, Afghanistan, contributed to this article.

Write to Michael M. Phillips at michael.phillips@wsj.com