The Nato-led force said that General Stanley McChrystal, the US and Nato commander in Afghanistan, had apologised to Hamid Karzai, the Afghan president, over the deaths.
Earlier, Karzai ordered an investigation into the incident near Marjah, which came after he had warned foreign forces to take all measures to protect civilians.
The Isaf statement quoted McChrystal as saying: "The current operation in central Helmand is aimed at restoring security and stability to this vital area of Afghanistan.
"It's regrettable that in the course of our joint efforts, innocent lives were lost.
"We extend our heartfelt sympathies and will ensure we do all we can to avoid future incidents," he said.
Nato and US officials had earlier hailed the success, so far, of Operation Moshtarak, meaning "together" in the local Dari language.
At least 27 fighters were reported to have been killed during the first day of fighting, while Nato said it had uncovered bomb-making materials and a weapons cache.
However, there will be concerns about the effect that civilian casualties will have on the long-term aim of keeping Marjah, a town of about 80,000 people in the central Helmand River valley, out of the hands of the Taliban and drug traffickers.
Al Jazeera's Zeina Khodr, reporting from the capital Kabul, said that a high death toll could cause the whole operation to "backfire".
"To win this war you are going to need the support of the people," she said.
"The Afghan government is facing a real test. It has to make good on promises of security and services in central Helmand."
Ali Ahmed Jalali, the former interior minister of Afghanistan, told Al Jazeera: "Marjah is a microcosm of the approach adopted by the international forces to clear an area and rebuild it and win the trust of the population.
"If the Marjah operations does lead to better stability in the area and if that is done properly, that will send a message to other parts of the country – but Marjah is only one of 385 districts in the country," he said.
James Bays, Al Jazeera's correspondent in Kabul, said: "It's very easy for the military to stage an operation like this, but they have to hold the territory.
"It is going to be very hard for them to recognise who is a member of the local population not fighting them and who is a member of the Taliban living there who does want to fight them."
At least 15,000 US, British and Afghan soldiers have been involved in operations around Marjah.
James Jones, the US president's senior security adviser, said in Washington that the offensive was "going very well".
"It's an important moment in time because this is the first time we put together all of the elements of the president's new strategy."
But US military officials acknowledged that it could take weeks to secure Marjah and the surrounding areas.
"That doesn't necessarily mean an intense gun battle, but it probably will be 30 days of clearing," Brigadier General Larry Nicholson said.
The Afghan and foreign troops have met only sporadic resistance from Taliban fighters, but have been targeted with improvised explosive devices and booby-traps.