Saudi and American officials are investigating the possibility that attacks on Saudi oil facilities Saturday involved cruise missiles launched from Iraq or Iran, questioning Yemeni rebel claims of responsibility, people familiar with the matter said.

Leaders of the Houthis, the Yemeni rebels whom Saudi Arabia is trying to dislodge from the country’s capital, claimed they sent a squad of drones hundreds of miles into the heart of Saudi Arabia to carry out coordinated attacks on two of the country’s vital energy sites. If true,...