The head of the Spanish region of Catalonia, Carles Puigdemont, said at least 80 people had been taken to hospital and around 12 had died, according to Reuters.
He said two people had been arrested. It was still not clear how many attackers had been involved.
Witnesses said the white van zigzagged at high speed down Las Ramblas, a busy avenue thronged with tourists, knocking down pedestrians and leaving bodies strewn across the ground.
Islamic State’s Amaq news agency said: “The perpetrators of the Barcelona attack are soldiers of the Islamic State and carried out the operation in response to calls for targeting coalition states” – a reference to a U.S.-led coalition against the Sunni militant group.
The claim could not immediately be verified.
If the involvement of Islamist militants is confirmed, it would be the latest in a string of attacks in the past 13 months in which they have used vehicles to bring carnage to the streets of European cities.
That modus operandi – crude, deadly and very hard to prevent – has killed well over 100 people in Nice, Berlin, London and Stockholm.
Witness Tom Gueller told the BBC: “I heard screams and a bit of a crash and then I just saw the crowd parting and this van going full pelt down the middle of the Ramblas and I immediately knew that it was a terrorist attack or something like that.
“It wasn’t slowing down at all. It was just going straight through the middle of the crowds,” he added.