BRUSSELS—A United Nations security group came under assault Wednesday while examining the site of an alleged chemical-weapons attack in Syria, international inspectors said, delaying an investigation into a strike that provoked a retaliatory Western military response.

The U.N. team was attacked with small-arms fire in the town of Douma, the Damascus suburb where Syrian forces allegedly unleashed a chemical-weapons attack on April 7, said the Organization for the Prohibition of Chemical Weapons, a fact-finding organization...