It is not clear that the United States is getting what it pays for. Mr. Karzai’s willingness to defy the United States — and the Iranians, for that matter — on an array of issues seems to have only grown as the cash has piled up. Instead of securing his good graces, the payments may well illustrate the opposite: Mr. Karzai is seemingly unable to be bought.

Over Iran’s objections, he signed a strategic partnership deal with the United States last year, directly leading the Iranians to halt their payments, two senior Afghan officials said. Now, Mr. Karzai is seeking control over the Afghan militias raised by the C.I.A. to target operatives of Al Qaeda and insurgent commanders, potentially upending a critical part of the Obama administration’s plans for fighting militants as conventional military forces pull back this year.

But the C.I.A. has continued to pay, believing it needs Mr. Karzai’s ear to run its clandestine war against Al Qaeda and its allies, according to American and Afghan officials.

Like the Iranian cash, much of the C.I.A.’s money goes to paying off warlords and politicians, many of whom have ties to the drug trade and, in some cases, the Taliban. The result, American and Afghan officials said, is that the agency has greased the wheels of the same patronage networks that American diplomats and law enforcement agents have struggled unsuccessfully to dismantle, leaving the government in the grips of what are basically organized crime syndicates.

The cash does not appear to be subject to the oversight and restrictions placed on official American aid to the country or even the C.I.A.’s formal assistance programs, like financing Afghan intelligence agencies. And while there is no evidence that Mr. Karzai has personally taken any of the money — Afghan officials say the cash is handled by his National Security Council — the payments do in some cases work directly at odds with the aims of other parts of the American government in Afghanistan, even if they do not appear to violate American law.

Handing out cash has been standard procedure for the C.I.A. in Afghanistan since the start of the war. During the 2001 invasion, agency cash bought the services of numerous warlords, including Muhammad Qasim Fahim, the current first vice president.