U.S. Marines are making steady progress in one of the biggest NATO offensives in Afghanistan since the war began in 2001, but areas infested with roadside bombs are bogging them down, a spokesman said on Monday.

The assault 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.

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.

Afghan officials said on Sunday that as many as 35 militants had been killed in the first two days of the offensive.

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, Sipe said.

Afghan officials said there had been some fighting.

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.

EARLY PROGRESS

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 must be effective enough to keep the Taliban from returning.

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.

Highlighting the dangers of fighting a resilient and unpredictable enemy, Helmand Province Governor Gulab Mangal said three would-be suicide bombers were gunned down on Sunday while trying to blow themselves up among troops.

The situation moment by moment is going the way the government had expected. The forces are extending their advances from points they have captured and the operation is going on successfully, he told a news conference.

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 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.

U.S. commanders are under pressure to deliver results on the battlefield in time for the start of the troop drawdown due in 2011.

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 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.

(Additional reporting by Abdul Malek in Lashkar Gah and Sayed Salahuddin and Michael Georgy in KABUL; Writing by Michael Georgy; Editing by Bryson Hull and Ron Popeski)