In a former high school classroom in this northeastern Syrian town, about 250 Arab recruits for the U.S.-backed war against the Islamic State were being prepped by Kurdish instructors to receive military training from American troops.

Most of the recruits were from villages surrounding the Islamic State’s self-
proclaimed capital of Raqqa, and the expectation is that they will be deployed to the battle for the predominantly Arab city, which is now the main target of the U.S. military effort in Syria.

But first, said the instructors, the recruits must learn and embrace the ideology of Abdullah Ocalan, a Kurdish leader jailed in Turkey whose group is branded a terrorist organization by both Washington and Ankara.

The scene in the classroom captured some of the complexity of the U.S.-backed fight against the Islamic State in Syria, where a Kurdish movement that subscribes to an ideology at odds with stated U.S. policy has become America’s closest ally against the extremists.