KABUL—The U.S. suffered a major blow in Afghanistan as President Hamid Karzai made a surprise demand that the American-led coalition pull its troops from villages back to bases, opening a new rift that threatens the U.S. strategy in the country.

U.S. officials said they are planning no changes in deployments, however, and played down Mr. Karzai's request, which came as Defense Secretary Leon Panetta left Kabul after meetings officials described as cordial.

The...