A presidential office statement that followed a meeting of Afghanistan's National Security Council also demanded an immediate halt to special forces activity in Wardak province west of Kabul, a hub counterinsurgency operations.
The action comes after Karzai last week banned his forces from calling in NATO airstrikes in populated areas, citing civilian casualties. The announcement also is playing out as the White House and NATO leaders ponder their troop commitments to Afghanistan after the coalition finishes its combat mission here at the end of 2014.
In some of the latest fighting, Taliban suicide bombers targeted Afghan security forces in three separate attacks Sunday, while the country's intelligence agency said it prevented a similar strike in the capital's diplomatic enclave.
Four members of the Afghan security forces and one civilian were reported killed in the attacks.
The U.S.-led coalition in Afghanistan said in a statement that it takes abuse allegations seriously.
Karzai's blunt statement did not provide specific evidence or mention any judicial determinations.
"After a thorough discussion, it became clear that armed individuals named as U.S. special forces stationed in Wardak province engage in harassing, annoying, torturing and even murdering innocent people," the statement said.
"A recent example in the province is an incident in which nine people were disappeared in an operation by this suspicious force," it said. In a separate incident, "a student was taken away at night from his home," it said, and his "tortured body with throat cut was found two days later under a bridge."
The statement noted, however, that "Americans reject having conducted any such operation and any involvement of their special force."