NATO troops have launched an offensive against the Taliban's last big strongholds in Afghanistan's most violent province, Helmand.
The 15,000-troop operation is the start of a campaign to impose government control on rebel-held areas this year, before US forces start to withdraw in 2011.
The area in southern Helmand has been beset by violence since the fall of the Taliban regime.
Marjah is today the target of the biggest military assault since the 2001 invasion, with Afghan President Hamid Karzai calling on Taliban fighters to lay down their arms and to rejoin mainstream Afghan society.
'President Karzai calls upon all Afghan Taliban to use this as an opportunity to renounce violence and re-integrate into civilian life alongside other Afghans for the welfare of their country,' said a statement issued by his office.
He also warned troops to avoid civilian casualties, and 'instructed all Afghan and international troops to exercise absolute caution to avoid harming civilians'.
The campaign had been highly publicised to allow civilians to leave the combat area and in the hope that many insurgents might choose not to fight.
Operation Mushtarak (Together), which was launched this morning, is a major test of US President Barack Obama's strategy to end the eight-year war against the Taliban, defeat al-Qaeda and hand greater control to the Western-backed Afghan government.
Within hours of the operation getting under way, US Marines at the tip of the assault battled with Taliban militants in Marjah.
Marines engaged in a firefight with Taliban militants after the US troops landed in helicopters near the town in the early morning hours.
They fired at least four rockets at militants who attacked from compounds.
More than two hours later, the area was still gripped by the firefight, with the Marines firing another large rocket.
Large explosions were also heard with a black plume of smoke seen rising into the sky.
British troops flew into the northern part of the surrounding Nad Ali district, followed by tanks and combat engineering units.
'The first phase of the operation is proceeding very successfully. The Taliban have heavily booby-trapped the area, but there has not been any fierce fighting yet,' Helmand Governor Gulab Mangal told a news conference.
'We have seized 11 key locations in the district and the resistance from the insurgents has been subdued.'