KABUL, Afghanistan — President Hamid Karzai acknowledged Monday that the Central Intelligence Agency has been dropping off bags of cash at his office for a decade, saying the money was used for “various purposes” and expressing gratitude to the United States for making the payments.

Mr. Karzai described the sums delivered by the C.I.A. as a “small amount,” though he offered few other details. But former and current advisers of the Afghan leader have said the C.I.A. cash deliveries have totaled tens of millions of dollars over the past decade and have been used to pay off warlords, lawmakers and others whose support the Afghan leader depends upon.

The payments are not universally supported in the United States government. American diplomats and soldiers expressed dismay on Monday about the C.I.A.’s cash deliveries, which some said fueled corruption. They spoke privately because the C.I.A. effort is classified.

Others were not so restrained. “We’ve all suspected it,” said Representative Jason Chaffetz, Republican of Utah and a critic of the war effort in Afghanistan. “But for President Karzai to admit it out loud brings us into a bizarro world.”