Nato has confirmed that two rockets fired at militants during its offensive in Helmand, south Afghanistan, missed their target and killed 12 civilians.
The rockets struck a house in Marjah as thousands of Nato troops continued their operations to oust the Taliban.
Nato's commander Gen Stanley McChrystal said that "we deeply regret this tragic loss of life".
Coalition forces are aiming to build on gains in Operation Moshtarak, tackling snipers and booby-traps on day two.
A third Nato death related to the operation has also been confirmed.
Operation Moshtarak, meaning "together" in the Dari language, is the biggest coalition attack since the Taliban fell in 2001.
The operation is also the first big test of US President Barack Obama's new "surge" strategy for Afghanistan.
Rocket system suspended
Civilian casualties have been a key concern for the Nato-led offensive.
The regions targeted were leafleted well in advance to minimise casualties.
President Hamid Karzai has called for an investigation into the civilian deaths, his office said.
The office said in a statement that it believed at least 10 of those killed were from the same family.
Nato said in a statement: "Two rockets from a High Mobility Artillery Rocket System launched at insurgents firing upon Afghan and [Nato] forces impacted approximately 300 metres (980ft) off their intended target, killing 12 civilians."
Gen McChrystal said: "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."
The use of the the rocket system involved has been suspended pending a review.
The BBC's Frank Gardner in Kandahar says the deaths are very damaging for a campaign aimed at protecting the local population and driving a wedge between them and the insurgents.
He says it is exactly the kind of incident that Afghanistan leaders had said must be avoided and which they know can play straight into the Taliban's hands.
The Ministry of Defence has said that British troops were not involved in the incident.
Meanwhile, US, UK and Afghan forces have faced gun battles and numerous booby-traps on day two of the offensive in Marjah and Nad Ali in Helmand province.
In Marjah, US Marine commander Brig Gen Larry Nicholson told Agence France-Presse his forces had "blown up a lot of IEDs" and come up against "a lot of sniper fire".
He said it could take up to 30 days to make the area safe.
Marines were fired upon during a ceremony to raise the Afghan flag in Marjah.
Another Marines spokesman, Lt Josh Diddams, told Associated Press that US forces were in the "majority of the city".
"We're starting to come across areas where the insurgents have actually taken up defensive positions. Initially it was more hit and run."
Nato officers and Afghan troops are holding shuras (meetings) with tribal leaders, and plan to bring in hundreds of Afghan police in the coming days to help secure the captured areas.
Casualties
Operation Moshtarak began before dawn on Saturday when more than 15,000 troops flew into central Helmand.
HAVE YOUR SAY The "surge" approach drove most of the insurgents out of Iraq and there is no reason why it shouldn't work in Afghanistan Alan Trent, London
American forces, led by 4,000 Marines, are focusing on Marjah, while 4,000 British troops are in Nad Ali.
A large Afghan force, as well as Canadians, Danes and Estonians, is also involved.
Three Isaf deaths related to Operation Moshtarak have been confirmed.
On Saturday, a British soldier, Lance Sergeant David Greenhalgh of 1st Battalion Grenadier Guards, died in an improvised explosive device (IED) attack, while a US soldier was killed by gunfire in Marjah.
On Sunday, another service member was killed in an IED attack.
At least 20 Taliban fighters were killed and another 11 detained on Saturday, an Afghan commander said.
'Going well'
At a Ministry of Defence briefing in London on Sunday, Maj Gen Gordon Messenger said the operation overall had so far "gone to plan".
"Nothing has stopped the mission from progressing," he said, although UK troops had taken small-arms fire.
AFP quoted President Obama's top security adviser, Gen James Jones, as also saying the offensive was "going well".
President Obama will be briefed on Sunday by the US commander in Afghanistan, Gen Stanley McChrystal.
