Days after Afghan President Hamid Karzai and President Obama seemed to agree on the future role of U.S. forces in Afghanistan, a division has emerged over one of the American military’s most prized defense programs.

Top Afghan officials said Obama’s pledge last week to remove U.S. troops from Afghan villages should apply to Special Operations forces charged with training the Afghan Local Police. But U.S. officials said they assumed that the policy would apply only to traditional military operations and would include an exemption for the police trainers, whose mission they see as critical to security throughout Afghanistan.