Volkswagen AG conceded it won’t be able sell diesel-powered vehicles in the U.S. for a prolonged period, withdrawing a request for regulators to certify new models in the wake of an emissions-cheating scandal.

Volkswagen’s 2016 model-year diesel-powered vehicles include emissions-control software that requires regulatory approval in the U.S., according to prepared remarks by the auto maker’s U.S. chief executive to be delivered on Thursday at a congressional hearing. The testimony doesn’t make clear whether the software can...