SHARM EL-SHEIKH, Egypt — Yemen’s embattled president on Saturday called Shiite rebels who forced him to flee the country “puppets of Iran,” directly blaming the Islamic Republic for the chaos there and demanding airstrikes against rebel positions continue until they surrender. Egypt’s president called for a regional Arab military force and a Gulf diplomat warned that Saudi-led airstrikes in Yemen could go on for months, raising the specter of a regional conflict pitting Sunni Arab nations against Shiite power Iran. The comments by Arab leaders including Yemeni President Abdel Rabbo Mansour Hadi, who fled his country only days earlier, came at an Arab summit largely focusing on the chaos there caused by the advance of the rebels, known as Houthis. Leaders of Egypt, Saudi Arabia and Kuwait obliquely referenced Iran earlier at the summit held in Egypt’s Red Sea resort of Sharm el-Sheikh.