House leaders set plans to question two key State Department witnesses after Secretary of State Mike Pompeo sought Tuesday to block the effort, in the first clash between congressional Democrats and the Trump administration of the newly minted impeachment inquiry.

Marie Yovanovitch, the former U.S. ambassador to Ukraine, will be deposed Oct. 11, postponing her scheduled session by nine days, a committee aide said Tuesday. Kurt Volker, the U.S. special representative for Ukraine negotiations who resigned last week, will be...