A Democratic senator urged fellow lawmakers to stop blocking votes on Trump administration ambassadorial nominees, arguing that the absence of ambassadors in key countries is hurting American diplomacy.

Sen. Chris Coons of Delaware, a member of the Senate Foreign Relations Committee, specifically called for a confirmation vote on Richard Grenell, the Trump administration’s nominee for ambassador to Germany, who has been in limbo since being nominated last fall. Mr. Grenell served as communications director for the U.S. mission...