"Stressing the need to protect the lives and property of civilians, President Karzai once again reminded the international forces to make every effort to avoid incidents that lead to civilian casualties," Karzai's office said in a statement.
Karzai, facing an election in August and eager to win over voters, ordered an investigation.
The U.S. military said the video was taken by a stationary balloon equipped with a camera. Such balloons are anchored at or near many coalition forward operating bases.
The military has been reluctant to release videos of combat operations, saying that such action could expose combat tactics or surveillance and intelligence-gathering methods.
Unmanned aircraft watch over U.S. convoys and combat units for hours at a time. Cameras on the drones take close-up video, day and night, that captures firefights, airstrikes and attacks on convoys and U.S. ground units.
But for security reasons, such video is rarely released, even in disputed incidents involving disturbing allegations against coalition forces.
Times staff writer Julian E. Barnes in Washington contributed to this report.