BARCELONA—A terrorist mowed down pedestrians with a van in the heart of Spain’s second-largest city on Thursday, killing at least 13 people in an attack claimed by Islamic State.

More than 100 others were injured, many so severely that the death toll could rise, according to Joaquim Forn, the Catalan region’s interior minister. The speeding, weaving vehicle left a trail of motionless bodies, some in pools of blood, on Las Ramblas, a central thoroughfare popular with both tourists and residents.

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