A quick and successful offensive by Kurdish fighters and allied rebels in a northern Syrian town has boosted a U.S.-backed effort to choke off Islamic State’s supply routes and offered a template for regaining territory from the extremist group.

Emboldened by the recapture of Tal Abyad, the Syrian Kurdish alliance said Tuesday that its next target is Raqqa, Islamic State’s main stronghold in Syria about 50 miles south of Tal Abyad. The fighters said they had already begun advancing southward toward Raqqa on Monday, reaching...