The U.S. is expanding its role in Saudi Arabia’s campaign in Yemen, vetting military targets and searching vessels for Yemen-bound Iranian arms amid growing concerns about the goals of the Saudi-led mission, according to U.S. and Arab officials.

U.S. officials worry mounting civilian casualties will undermine popular support in Yemen and in other Sunni Arab countries backing the campaign. At least 648 civilians have been killed since the intervention began, and Saudi-led strikes have hit hospitals, schools, a refugee camp...