Five Afghan officers were wounded, The New York Times reported. The police were at a checkpoint in Nangarhar in eastern Afghanistan.
"The American troops were coming toward the Afghan police post as both sides did not know the identity of each other," said Nasir Ahmad Safi, a police official in Nangarhar.
Afghan officials said police, who had not been notified U.S. troops would be operating the area, began the shooting. The U.S. forces, thinking they were under attack by insurgents, called in air support.
Karzai, in a statement, said the deaths were part of a "heartbreaking incident" caused by a lack of cooperation between U.S. and other coalition troops and Afghan forces, The Telegraph reported. The British newspaper said that eight police officers died.