Islamic State fighters intensified their advance in recent days on a town in northern Syria close to a vital supply route for Syrian rebels near the border with Turkey, according to opposition rebels and local residents.

A number of rebel factions are struggling to stave off the militants, who have been gradually encircling the town of Marea about 15 miles south of the Turkish border. Marea is a key town along a 60-mile stretch of the border that Turkey and the U.S. want to clear of Islamic State fighters and the group’s...