NATO forces say more than 10 civilians have been killed after a rocket fired at Taliban fighters veered off course.
Afghan President Hamid Karzai expressed sadness at the incident and urged NATO to exercise caution.
However, the 15,000 strong battle group continues to advance into the Taliban strongholds of Marjah and Nad Ali.
Military planners expect Operation Moshtarak to take up to a month.
Marjah has long been a base for insurgents and the lucrative poppy trade, which the West believes funds Taliban activity.
Colonel Matt Bazeley of the British Army’s 28 Engineer Regiment is involved in operations in Helmand. He said: “They’ve all left the area, what was their drugs capital and what was their IED centre has been abandoned by the Taliban and we are just opening this route and now we can press on and clear the whole area.”
Meanwhile, the US Chairman of the Joint Chief of Staffs, Admiral Mike Mullen has been holding talks in the Egyptian capital Cairo.
He stressed the role the Afghan army are playing in the offensive.
“The operation is Afghan led. We are in partnership with them but really the Afghans are leading the operation, which is critical,” he said.
The More than 30 transport helicopters ferried troops into the heart of Marjah at dawn on Saturday as night pictures filmed from a British Tornado illustrate.