WASHINGTON—A senior State Department official went before House impeachment investigators Saturday and said that top officials stymied a show of solidarity for the former U.S. ambassador to Ukraine after President Trump had her removed, according to a person familiar with his closed-door testimony.

Philip Reeker, the acting assistant secretary of state in the Bureau of European and Eurasian Affairs, was also present for a White House interagency meeting during which a Department of Defense official raised concerns about a...