The assault, one of NATO's biggest against the Taliban since the Afghan war began in 2001, is the first test of U.S. President Barack Obama's plan to send 30,000 more troops to seize insurgent-held areas ahead of a planned 2011 troop drawdown.
"There were bombardments in parts of Marjah and as a result 12 Taliban have been killed," Dawud Ahmadi, a spokesman for the provincial governor of Helmand, told reporters.
The United States' top military officer on Sunday said the assault on the Taliban stronghold of Marjah in Afghanistan's Helmand province had got "off to a good start."
"It's actually very difficult to predict (the end)," Admiral Mike Mullen, chairman of the U.S. Joint Chiefs of Staff, told reporters during a visit to Israel. "We have from a planning standpoint talked about a few weeks, but I don't know that."
The attack started on Saturday with waves of helicopters ferrying troops into Marjah and the nearby Nad Ali district. The next day, U.S. Marines came under intense fire in the heart of Marjah.
NATO rockets killed 12 Afghan civilians on Sunday in the second day of an offensive designed to impose Afghan authority on one of the last big Taliban strongholds in the country's most violent province.
The offensive has been flagged for weeks, to persuade Taliban fighters to leave so the area can be recaptured with minimal damage or loss of civilian life, in the hope that the roughly 100,000 people there will welcome the Afghan administration.
