“Hundreds of millions of dollars in drug money are flowing through the southern region, and nothing happens in southern Afghanistan without the regional leadership knowing about it,” a senior American military officer in Kabul said. Like most of the officials in this article, he spoke on the condition of anonymity because of the secrecy of the information.

Image Ahmed Wali Karzai, right, the brother of President Hamid Karzai of Afghanistan, at a campaign event in Kandahar in August. Credit... Banaras Khan/Agence France-Presse — Getty Images

“If it looks like a duck, and it quacks like a duck, it’s probably a duck,” the American officer said of Mr. Karzai. “Our assumption is that he’s benefiting from the drug trade.”

American officials say that Afghanistan’s opium trade, the largest in the world, directly threatens the stability of the Afghan state, by providing a large percentage of the money the Taliban needs for its operations, and also by corrupting Afghan public officials to help the trade flourish.

The Obama administration has repeatedly vowed to crack down on the drug lords who are believed to permeate the highest levels of President Karzai’s administration. They have pressed him to move his brother out of southern Afghanistan, but he has so far refused to do so.

Other Western officials pointed to evidence that Ahmed Wali Karzai orchestrated the manufacture of hundreds of thousands of phony ballots for his brother’s re-election effort in August. He is also believed to have been responsible for setting up dozens of so-called ghost polling stations  existing only on paper  that were used to manufacture tens of thousands of phony ballots.

“The only way to clean up Chicago is to get rid of Capone,” General Flynn said.

In the interview in which he denied a role in the drug trade or taking money from the C.I.A., Ahmed Wali Karzai said he received regular payments from his brother, the president, for “expenses,” but said he did not know where the money came from. He has, among other things, introduced Americans to insurgents considering changing sides. And he has given the Americans intelligence, he said. But he said he was not compensated for that assistance.