Authorities are looking for Younes Abouyaaqoub, a 22-year-old they believe was behind the wheel of a van which left a trail of dead and injured on Barcelona's famed boulevard.
European police forces were now searching for Abouyaaqoub, the Catalan region government said on Monday.
They did not rule out that the suspect had slipped across the border into France.
"This person is no longer just being sought in Catalonia, but in all European countries, this is an effort by European police," Joaquim Forn, home affairs chief in the northeastern Spanish region, told Catalan radio.
Forn confirmed that police were almost certain Abouyaaqoub was the driver.
Abouyaaqoub allegedly abandoned the van after zig-zagging down Las Ramblas avenue at high speed, police have said.
Witnesses claimed to have seen a man walking away unarmed from the scene.
Authorities have stepped up checks at Spain's borders.
The other suspects in a cell of 12 people thought to be behind the attack have been arrested, shot by police or killed in an explosion at a house in Catalonia a day before Thursday's van attack.
The attack in Barcelona was linked to another outburst of violence hours later in the resort down of Cambrils, further down the Mediterranean coastline from Barcelona.
A car crashed into passers-by there, and attackers reportedly got out to tried and stab people. Five suspects were shot dead, while a Spanish woman died in the attack.
Source: News agencies