More than 15,000 American, British and Afghan troops have launched the biggest offensive in Afghanistan since the overthrow of the Taliban in 2001.
Helicopter-borne forces are attacking the Taliban-held districts of Marjah and Nad Ali in Helmand province in a bid to re-establish government control.
Nato says Marjah is home to the biggest community under insurgent control in the south and 400 to 1,000 militants. '
Many residents fled ahead of Operation Moshtarak - meaning "together" in Dari.
Nato had distributed leaflets in the Marjah area warning of the planned offensive in a bid to limit civilian casualties. Villagers said they warned Taliban fighters to leave the area or be killed.
Despite the warnings, reports from Helmand suggest many civilians remain, while the Taliban has claimed its fighters are ready to resist the assault.
It is thought the Taliban will have prepared defences, and planted many improvised explosive devices (IEDs) on the routes they expect troops to take.
Earlier this week British forces began a "softening up" process, taking part in a Nato ground and air offensive on insurgent positions.
On Thursday a British soldier involved in Operation Moshtarak was killed by an IED, and UK Defence Secretary Bob Ainsworth has warned that there will be more casualties in the coming days.
'First wave'
Operation Moshtarak is being led by the US Marine Corps, but a total of 4,000 British troops are involved on the ground and in support, supported by Danes and Estonians.
The initial offensive in Marjah, in Nad Ali district, began early on Saturday.
More than 4,000 US marines, 1,500 Afghan soldiers and 300 US soldiers moved in by helicopter under cover of night.
The assault was preceded by illumination flares, which were fired over the town at about 0200 local time (2130 GMT on Friday ), the Associated Press reported.
"The first wave of choppers has landed inside Marjah. The operation has begun," said Capt Joshua Winfrey, commander of Lima Company, 3rd Battalion, 6th Marines, which was at the forefront of the attack.
For the first time Afghan forces have been at the forefront of planning and will share the burden of the fighting. More than 1,900 Afghan police will provide support after the initial military operations end, and a large team of Afghan administrators have been assembled.
"We are in this together. We planned it together; we will fight it together; we will see it through together. Afghans with allies; soldiers with civilians; government with its people," the commander of British forces in Helmand, Brig James Cowan, told his troops on Thursday.
"Soon we will clear the Taliban from its safe havens in central Helmand. Where we go, we will stay. Where we stay, we will build."
'Tipping point'
A senior Nato official told the BBC that Afghanistan's President, Hamid Karzai, had approved the start of the offensive on Thursday.
The official said it was "probably the definitive operation" of the counter-insurgency strategy outlined last year by the commander of both Nato and US forces in Afghanistan, Gen Stanley McChrystal.
"If it goes well, this operation could potentially define the tipping point, the crucial momentum aspect in the counter-insurgency," the official said. "We are going to take this place and take it very hard."
The decision to go into Marjah is part of an effort to secure a 320km (200-mile) horseshoe-shaped string of towns that runs along the Helmand River, through Kandahar and on to the Pakistani border. The area holds 85% of the population of Kandahar and Helmand.
The BBC's Adam Brookes says the offensive has political importance in Washington because it is by far the largest single operation since President Barack Obama announced a "surge" in December, increasing the number of US troops in the country by 30,000 to nearly 100,000.
Marjah, which lies in Helmand's "green zone" - an irrigated area of lush vegetation and farmland - is a hive of Taliban activity and is a centre for cultivation of opium poppies.
Once the area is secured, Nato hopes to provide aid and to restore public services in the area. The aim, the alliance says, is to win support among the estimated 125,000 people who live there and prevent the Taliban from regaining control.
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