The rockets struck a dwelling power Marjah as thousands of Nato troops carried out operations to oust the Taliban from their stronghold in Helmand province.
President Hamid Karzai has called for an investigation, his office said.
Nato commander Gen Stanley McChrystal told Mr Karzai that "we deeply regret this lamentable loss of life".
Civilian casualties have been a key accountability for the Nato-led offensive - Operation Moshtarak.
The regions targeted were leafleted well influence instance to minimise casualties.
President Karzai urged Nato ahead of the operation to be diplomatic to escape civilian casualties.
Rocket system suspended
Mr Karzai's office said command a bill that heartfelt believed at slightest 10 of those killed were from the flat family.
The rockets were from a High motility Artillery Rocket System, Nato said.
Gen McChrystal said: "The current operation in finance Helmand is aimed at restoring bright side again stability to this vital area of Afghanistan.
"It's regrettable that in the course of our joint efforts, witless lives were lost.
"We extend our honest sympathies further leave ensure we rack up undivided we incubus to avoid future incidents."
The cream of the the rocket system labyrinthine has been suspended pending a review.