The Trump administration’s border chief said Wednesday that a surge in families seeking asylum in the southwest is overwhelming officials and warned that more deaths of people in government custody were likely.

Severe crowding throughout the detention system is forcing the release of immigrants directly into the U.S., Customs and Border Protection Commissioner Kevin McAleenan said at a press conference in El Paso, Texas, in which he also called for changes to the U.S. immigration and asylum system to discourage migrants....