Nine children and three women were among the dead. The killing spree deepened a crisis between US forces and their Afghan hosts over Americans burning Muslim holy books on a base in Afghanistan.
The burnings sparked weeks of violent protests and attacks that left some 30 people dead. Six US service members have been killed by their Afghan colleagues since the Quran burnings came to light, but the violence had just started to calm down.
"This is an assassination, an intentional killing of innocent civilians and cannot be forgiven," Karzai said in a statement.
He said he has repeatedly demanded the US stop killing Afghan civilians. The violence over the Quran burnings spurred calls in the US for a faster exit strategy from the 10-year-old Afghan war. President Barack Obama even said recently that "now is the time for us to transition."
But he also said he had no plan to change the current timetable that has Afghans taking control of security countrywide by the end of 2014.
The tensions between the two countries had appeared to be easing as recently as Friday, when the US and Afghan governments signed a memorandum of understanding about the transfer of Afghan detainees to Afghan control a key step toward an eventual strategic partnership to govern US forces in the country. But today's shooting could push that agreement further away.
"This is a fatal hammer blow on the US military mission in Afghanistan. Whatever sliver of trust and credibility we might have had following the burnings of the Quran is now gone," said David Cortright, the director of policy studies at Notre Dame's Kroc Institute for International Peace Studies and an advocate for a quick withdrawal from Afghanistan.