Iraq wants its neighbors to talk to each other rather than settle scores on its territory.
Relations within the region are chiefly strained by hostility between Iran on one side and the United States and its Arab Gulf allies on the other.
Heads of state attending included Egypt's President Abdel Fattah al-Sisi, King Abdullah of Jordan, and Qatari Emir Sheikh Tamim bin Hamad al-Thani.
Kuwait and the UAE sent their heads of government and Turkey its foreign minister.
Shi'ite Muslim Iran and Sunni Saudi Arabia, longtime rivals for regional dominance, did not send their heads of state or government. Iran said it was sending Foreign Minister Hossein Amirabdollahian, while Saudi Arabia had not yet announced its representative.
Organisers said they did not expect any diplomatic breakthroughs at the summit.