Many Arab governments grumbled quietly in 2011 as the United States left Iraq, fearful it might fall deeper into chaos or Iranian influence. Now, the United States is back and getting a less than enthusiastic welcome, with leading allies like Egypt, Jordan and Turkey all finding ways on Thursday to avoid specific commitments to President Obama’s expanded military campaign against Sunni extremists…

The tepid support could further complicate the already complex task Mr. Obama has laid out for himself in fighting the extremist Islamic State in Iraq and Syria: He must try to confront the group without aiding Syria’s president, Bashar al-Assad, or appearing to side with Mr. Assad’s Shiite allies, Iran and the militant group Hezbollah, against discontented Sunnis across the Arab world.

While Arab nations allied with the United States vowed on Thursday to “do their share” to fight ISIS and issued a joint communiqué supporting a broad strategy, the underlying tone was one of reluctance. The government perhaps most eager to join a coalition against ISIS was that of Syria, which Mr. Obama had already ruled out as a partner for what he described as terrorizing its citizens.