These involved the vehicles plowing into pedestrians in Barcelona and Cambrils.
Canadian Prime Minister Justin Trudeau expressed his grief over the Barcelona terror attack which claimed at least 13 lives and injured dozens others on Thursday.
Of the 12 people police suspect of involvement in the attacks, five were shot dead by security forces in Cambrils and another four have been arrested, said Josep Lluis Trapero of Catalonia's police during a television interview late Friday.
While Secretary of State Rex Tillerson did not immediately identify the American killed in the attack, Bay Area resident Dan Tucker later confirmed that it was his 43-year-old son Jared who had died.
On Thursday and early Friday, Barcelona and Cambrils in Catalonia were hit by two van ramming attacks, which have killed 15 people and left over 130 more injured.
Spanish police said they initially thought the blast in the small coastal town of Alcanar, which killed at least one person and injured seven, was connected to a clandestine drugs laboratory.
Authorities have issued arrest warrants for four further suspects in connection with the two attacks, a judicial source said, declining to give their names. Foreign Minister Jean-Yves Le Drian said 28 French nationals had been injured, with eight of them in a serious condition.
Now the street is perhaps even more crowded than it was at the time of the attack, tens of thousands of people have come here.
Trapero said investigators believe those who acted were survivors from a gang that had been planning for weeks to carry out a bombing attack - but that they chose to use a van after their components blew up.
A woman subsequently died from her injuries, Catalan emergency services said, taking the number of dead in both attacks to 14.
"The only thing we can do is go forward with peace and goodness", he said. One is just 17 years old.
"We saw a white van collide with people". Neither man is believed to be the driver.
Catalan police later said they found an ax and knives in the vehicle, and the attackers had fake explosive belts attached to them.
Police now believe the accidental detonation of homemade butane bombs forced the perpetrators to alter the plans and timing for their attack. They also said they had arrested four suspects - three Moroccans and a Spaniard.
But Lea warned that terror threats were consistent in most big Western European cities, saying that the next serious attack "could pop up easily in Birmingham, Berlin or Barcelona".
The dual attacks unnerved a country that hasn't seen an Islamic extremist attack since 2004, when al-Qaeda-inspired bombers killed 192 people in co-ordinated assaults on Madrid's commuter trains.
Then just eight hours later attackers struck again in the early hours of today morning, this time in the seaside resort of Cambrils where an Audi A3 vehicle rammed into pedestrians, injuring six civilians and a police officer. Two Italians were the first of the deceased victims to be named.