"The US special forces and illegal armed groups created by them are causing insecurity, instability, and harass local people in this province," he told a press conference.
The announcement would be another blow to the prestige of US-led forces as they prepare to withdraw combat troops from the war against Taliban Islamist insurgents by the end of next year.
The bulk of NATO's 100,000 troops are due to leave Afghanistan by the end of 2014.
A US Forces Afghanistan (USFOR-A) spokesman said he was aware of the reported comments by Faizi.
"We take all allegations of misconduct seriously and go to great lengths to determine the facts surrounding them," he said.
"Until we have had a chance to speak with senior (Afghan) officials about this issue we are not in a position to comment further. This is an important issue that we intend to fully discuss with our Afghan counterparts."
More than 3,200 NATO troops, mostly Americans, have died in support of Karzai's government in the war since the Taliban were ousted by a US invasion in 2001, but relations between the president and the US are often prickly.