Administration officials had sought to avoid the appearance of another  American-dominated war, even as most leaders in the Persian Gulf  seem more preoccupied with supporting rebels fighting the government of President Bashar al-Assad of Syria.  Now, some of those officials note with resignation, the Arab partners have quietly left the United States to run the bulk of the air war in Syria — not the first time Washington has found allies wanting.

Saudi Arabia and the United Arab Emirates have shifted most of their aircraft to their fight against Iranian-backed Houthi rebels in Yemen. Jordan, reacting to the grisly execution of one of its pilots by the Islamic State, and in a show of solidarity with the Saudis, has also diverted combat flights to Yemen. Jets from Bahrain last struck targets in Syria in February, coalition officials said. Qatar is flying patrols over Syria, but its role has been modest.

“They’ve all been busy doing other things, Yemen being the primary draw,” Lt. Gen. Charles Q. Brown Jr., who leads the air war from a $60 million command center at this sprawling base in Qatar, said of the Arab allies, who he said still fly periodic missions in Syria and allow American jets to use their bases.