The assault is the first test of US President Barack Obama's plan to send 30,000 more troops to seize insurgent-held areas ahead of a planned 2011 troop drawdown.
"We are making steady progress but being very methodical about detecting and clearing routes in an area heavily saturated with IEDs (Improvised Explosive Devices)," Marine Capt. Abraham Sipe told Reuters in response to an email, adding counts of militants killed of captured would not be provided.
"In many parts of Marjah, we have seen very little opposition. There are areas where Marines have met with stiff resistance, but they are making steady progress throughout the area." Twelve Taleban fighters were killed overnight in a NATO offensive against the group's last stronghold in Afghanistan's most violent province, a provincial government official said.
"There were bombardments in parts of Marjah and as a result 12 Taleban have been killed," Dawud Ahmadi, a spokesman for the provincial governor of Helmand, told reporters.
Much of the success of the operation in Helmand province depends on whether the new administration wins the trust of the local population and Afghan troops are effective enough to keep the Taleban from returning.
Civilians have already expressed doubts that Afghan troops can keep control of the district if the Taleban are cleared.
At a meeting with government authorities close to Marjah, some 200 villagers urged the regional government to persuade NATO-led troops to remain in Marjah once they secure the area, Ahmadi said.
"They said that the Afghan forces do not have the ability to keep control of the area," Ahmadi said.
NATO and the Afghan government's credibility rests on limiting civilian casualties, especially since NATO commanders told Marjah residents to stay home during the offensive which could last weeks.
NATO rockets killed 12 Afghan civilians on Sunday on the second day of an offensive designed to impose Afghan authority on one of the last big Taleban strongholds in the country's most violent province.
The offensive has been flagged for weeks to persuade Taleban 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.
Marjah has long been a breeding ground for insurgents and lucrative opium poppy cultivation, which Western countries say funds the insurgency.
The United States' top military officer on Sunday said the assault on Marjah had got "off to a good start.”
"It's actually very difficult to predict (the end)," Admiral Mike Mullen, chairman of the US 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, US Marines came under intense fire.
"There was fighting last night and some sporadic clashes are still going on in Marjah. The enemy has suffered casualties," said Ghulam Mahaiuddin Ghori, a senior Afghan army general in Helmand.
