The offensive began with waves of helicopters ferrying US Marines and members of the Afghan National Army into Marjah. British and Afghan troops then flew into Nad Ali district, to the north, followed by tanks and combat units.
On Saturday, Maj Gen Gordon Messenger told a briefing in London there had been "sporadic fighting" and the Taliban were unable to "put up a coherent response".
"The key objectives have been secured and have been done so with minimal interference," he said.
However, one British soldier, from the 1st Battalion Grenadier Guards, was killed by an explosion in Nad Ali. A US soldier was meanwhile killed by small-arms fire, officials said.
Prime Minister Gordon Brown praised the UK forces for their action.
He said: "This day will be long remembered as the day when a new phase of the campaign to win the support of the people of Afghanistan was initiated."
A White House spokesman said President Barack Obama was keeping a close eye on combat operations and had had multiple updates. He was also to be briefed by the top US commander in Afghanistan on Sunday morning.
MARJAH: 'TALIBAN STRONGHOLD'
Town and district about 40km (25 miles) south-west of Lashkar Gah
Lies in Helmand's 'Green Zone' - an irrigated area of lush vegetation and farmland
Last remaining major Taliban stronghold in southern Helmand
Area considered a centre for assembling roadside bombs
Key supply centre for opium poppies - lucrative revenue source for Taliban
Estimates of Taliban numbers range up to 1,000
Population of Marjah town put at 80,000 while the whole of Marjah district is thought to have 125,000
Afghan Defence Minister Gen Rahim Wardak also said it was important to bring in local security forces quickly.
He said there was a threat from booby-traps left by the Taliban.
"The area has been heavily mined, that's why we are moving so slowly," he said in Kabul.
US Marine ordnance units are working their way through Marjah, finding and exploding bombs. Three US soldiers were killed by an improvised explosive device in southern Afghanistan, Nato said, although was unclear if it was related to Moshtarak.
Marjah has also long been regarded as a linchpin of the lucrative network for smuggling opium - the raw ingredient used to make heroin - harvested from Helmand's poppy fields.
Nato had distributed leaflets in the area warning of the planned offensive in a bid to limit civilian casualties.
The operation is part of an effort to secure a 320-km (200-mile) horseshoe-shaped string of towns that runs along the Helmand River, through Kandahar and on to the Pakistani border.
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