Numerous reports link Ahmed Wali Karzai to the drug trade, according to current and former officials from the White House, the State Department and the United States Embassy in Afghanistan, who would speak only on the condition of anonymity. In meetings with President Karzai, including a 2006 session with the United States ambassador, the Central Intelligence Agency’s station chief and their British counterparts, American officials have talked about the allegations in hopes that the president might move his brother out of the country, said several people who took part in or were briefed on the talks.

“We thought the concern expressed to Karzai might be enough to get him out of there,” one official said. But President Karzai has resisted, demanding clear-cut evidence of wrongdoing, several officials said. “We don’t have the kind of hard, direct evidence that you could take to get a criminal indictment,” a White House official said. “That allows Karzai to say, ‘where’s your proof?’ ”

Image Heroin caches were found near Kandahar and Kabul. Credit... The New York Times

Neither the Drug Enforcement Administration, which conducts counternarcotics efforts in Afghanistan, nor the fledgling Afghan anti-drug agency has pursued investigations into the accusations against the president’s brother.

Several American investigators said senior officials at the D.E.A. and the office of the Director of National Intelligence complained to them that the White House favored a hands-off approach toward Ahmed Wali Karzai because of the political delicacy of the matter. But White House officials dispute that, instead citing limited D.E.A. resources in Kandahar and southern Afghanistan and the absence of political will in the Afghan government to go after major drug suspects as the reasons for the lack of an inquiry.

“We invested considerable resources into building Afghan capability to conduct such investigations and consistently encouraged Karzai to take on the big fish and address widespread Afghan suspicions about the link between his brother and narcotics,” said Meghan O’Sullivan, who was the coordinator for Afghanistan and Iraq at the National Security Council until last year.

It was not clear whether President Bush had been briefed on the matter.Humayun Hamidzada, press secretary for President Karzai, denied that the president’s brother was involved in drug trafficking or that the president had intervened to help him. “People have made allegations without proof,” Mr. Hamidzada said.