MARJAH, Afghanistan — Sniper teams attacked U.S. Marines and Afghan troops across the Taliban haven of Marjah, as several gunbattles erupted today on the third day of a major offensive to seize the extremists' southern heartland.

Multiple firefights broke out in different neighborhoods as American and Afghan forces worked to clear out pockets of insurgents and push slowly beyond parts of the town they have claimed. With gunfire coming from several directions all day long, troops managed to advance only 500 yards deeper as they fought off small squads of Taliban snipers.

"There's still a good bit of the land still to be cleared," said Capt. Abraham Sipe, a Marine spokesman. "We're moving at a very deliberative pace."

The massive offensive in the Marjah area — the largest Taliban stronghold and a key opium trafficking hub — involves about 15,000 U.S., Afghan and British troops and is the biggest joint operation since the 2001 U.S.-led invasion of Afghanistan.

Today, Afghan military officials gave a more optimistic view of the progress being made, with Brig. Gen. Sher Mohammad Zazai saying Afghan and NATO forces have largely contained the insurgents and succeeded in gaining trust from residents, who have pointed out mine locations.

"Today there is no major movement of the enemy. South of Marjah they are very weak. There has been low resistance. Soon we will have Marjah cleared of enemies," Zazai said at a briefing in Lashkar Gah, the provincial capital of Helmand province. He added only three Afghan troops had been injured.

Interior Minister Hanif Atmar said he expected some insurgent fighters had already fled the area in advance of the offensive, possibly heading to the Pakistan border.

The enemy "had ample time to flee. Our intention was known to both our public and the enemy," he said.

However, the mission faced a setback Sunday when two U.S. rockets slammed into a home outside Marjah, killing 12 civilians. NATO said today the rockets missed their target by about 600 meters, or about a third of a mile. NATO had earlier said the rockets missed their target by just 300 meters.

Six children were among the dead from the rocket strike, a NATO military official confirmed today, speaking on condition of anonymity because the information had not been formally released.

British Chief of the Defense Staff Air Chief Marshal Sir Jock Stirrup called the off-target strike a "very serious setback" in efforts to win the support of local communities.

"This operation ... is not about battling the Taliban. It is about protecting the local population and you don't protect them when you kill them," he said in an interview with the BBC.