The latest confrontation with Washington flared after the MCTF and the SIU last month, without Mr. Karzai's approval, raided the home of a senior Afghan presidential aide who had been taped while allegedly soliciting a bribe.
The scandal is threatening to become the most serious crisis in the U.S.'s relations with Mr. Karzai since the controversy over accusations of widespread fraud in the presidential elections a year ago. Mrs. Clinton phoned Mr. Karzai last week after he created a commission to oversee the MCTF and the SIU.
The rift over the agencies appears to have wiped out any residual goodwill from Mr. Karzai's May trip to Washington, where he was praised for his pledges to clean up the Afghan government.
Mr. Karzai has also had a stormy beginning with the new U.S.-led coalition commander, Gen. David Petraeus. U.S. commanders were upset last month when Mr. Karzai issued a statement condemning coalition forces for allegedly causing 52 civilian casualties in a rocket attack in Helmand. The coalition military says it had no record of carrying out such an attack—and that local hospitals had no record of such casualties from that area.
"The people who are working in private security companies are against Afghan national interest, and their salaries are illegal money. They are thieves during the day and terrorists during the night," Mr. Karzai said in Saturday's speech. "If they want to serve Afghanistan they have to join the Afghan police."
A coalition spokesman, U.S. Air Force Maj. Joel Harper, said the international forces are "working with the Afghan government to build its police capabilities and capacity so that private security companies are no longer required."
Many of the 52 registered security companies operating in Afghanistan are foreign, but some of the bigger ones are Afghan-owned, and have close links with prominent government officials and members of Mr. Karzai's family. They employ an estimated 30,000 people.
Private companies provide security for Western diplomatic missions and aid agencies, coalition installations, hotels and major infrastructure such as airports. They also guard supply convoys that bring vital goods to landlocked Afghanistan from neighboring countries.
Many Western government agencies and contractors operating in Afghanistan are wary of relying on the Afghan police force, which is often infiltrated by the Taliban.
"There aren't enough state or international security forces to provide all the services that private security companies do," said John Dempsey, an analyst at the U.S. Institute for Peace.
There is no firm deadline for shutting down the security firms, but Mr. Karzai wants them closed "as soon as possible," said the president's chief spokesman, Waheed Omar, on Saturday. "The process needs to start," he said.
In mid-July, the U.S. special representative for Afghanistan and Pakistan, Richard Holbrooke, had held up the MCTF in Senate testimony as proof of Mr. Karzai's seriousness in curbing graft. That followed a move in June by a congressional panel to freeze some $4 billion in aid to Afghanistan, after The Wall Street Journal reported that billions of dollars in cash—some of it in aid money—was being taken out each year through Kabul's international airport.
The Kabul offices of the financial company most prominent in this outflow, the New Ansari Exchange, were raided by the SIU in January. The company has connections with senior members of the Afghan government and some of Mr. Karzai's relatives.
New Ansari has denied any wrongdoing.
The presidential aide detained by the MCTF and SIU last month, Mohammed Zia Saleh, head of administration for Afghanistan's National Security Council, was taped while allegedly discussing a bribe in the form of a car for quashing an the New Ansari investigation.
Mr. Saleh, who has been freed on Afghan government orders, couldn't be located to comment.
According to Western and Afghan officials, the MCTF and SIU are working normally so far, and their sensitive investigation files—including those targeting senior government figures—haven't been taken by Mr. Karzai's commission, which is headed by Attorney General Ishaq Aloko.
Asked whether the files could be seized, an aide to Mr. Karzai said: "The president issued an order asking the commission to review all the cases, so it could happen."