Five Taliban fighters were killed during fighting in the last major Taliban stronghold in Helmand province on Saturday, after thousands of British and American troops attacked in the early hours.
An armada of helicopters ferried troops into the Marjah area of Nad-e-Ali district before dawn, and soldiers quickly engaged in sporadic firefights with waiting gunmen.
The operation, in a district which has become a hub of insurgent fighters, bomb-makers and opium-growers, has been described as the biggest of the war in Afghanistan.
Commanders said the force was making good progress against hundreds of Taliban fighters.
By noon on Saturday, Afghan generals said five Taliban fighters had been killed and eight more arrested without any casualties being suffered by the Nato or Afghan government forces. But Nato commanders have warned that there would "definitely be casualties" in the coming days.
The offensive has been widely trailed in an information war designed to warn civilians and demoralise a mixed defence of Afghan Taliban and foreign fighters.
Taliban fighters have turned the district, which is criss-crossed with irrigation canals, into what has been described as the biggest minefield Nato forces have ever ventured into.
While some troops were airlifted into the town at dawn, others punched through to the main canal on the outskirts of the town by mid-morning.
Gen Sher Mohammad Zazai, commander of the 205th Brigade, said that the early stages of Operation Moshtarak, which means "together", had been highly successful.
He said: "Definitely there will be casualties and fighting. Our operation so far is very successful. We have not faced any casualties.
"Five insurgents have been killed and we have arrested eight more. I am sure this number will get higher.
"Different types of bombs have been planted in the area."
He said that in the early stages of the operation there had been little Taliban resistance.
The operation is the largest yet of the Afghan war, and aims to break the back of the Taliban insurgency in Helmand province.
It followed two days of shuras, meetings with local elders, in which the Afghan government and international forces sought help from leaders of the 120,000 residents of the district.
Nato signalled the offensive for weeks before its start, and in turn the Taliban announced that they would fight a classic guerrilla campaign instead of standing and fighting. They have promised to melt into the civilian population to continue their fight.
British and US commanders estimated that many of up to 1,000 fighters who had been based in the district may have slipped away in recent days.
Gulab Mangal, governor of Helmand, said the shura had decided on Friday that the assault should take place as soon as possible, though elders pleaded with the British and US to minimise civilian casualties.
There were no airstrikes in the early hours of the assault, in line with Nato's policy of trying to avoid civilian casualties. Witnesses said the night had been lit by flares and missile strikes.
Residents told The Sunday Telegraph on the eve of the assault that they were terrified of being caught in the crossfire.
Pahlawan, a 28-year-old farmer from Marjah with only one name, said: "We are living like prisoners because all around Marjah there is fighting. We think our houses will be damaged and civilians will be killed."
Ahmad Zia, a 37-year-old farmer added: "I think this operation will take time because the Taliban have put a lot of landmines in the streets and in the roads.
"I think Marjah will be the scene of fighting for one year or more."