Younes Abouyaaqoub is understood to be the chief suspect for the attack on Las Ramblas that killed at least 13 dead and injured more than 130.
According to the Spanish newspaper El País, police in Catalonia said they were searching for the man, who is thought to be a key member of a 12-strong jihadist cell responsible for the attacks.
On Friday it emerged that another suspect, Moussa Oukabir, who is thought to have rented the van, was among five men shot dead as they launched a second attack in the coastal town of Cambrils.
The teenager, said to be 17 or 18 years old, is suspected of using his brother’s documents to hire the vehicle that ploughed through pedestrians in the Barcelona tourist hotspot on Thursday evening.
He reportedly died along with Said Aallaa, 19, and Mohamed Hychami, 24, who were part of a group that mounted a similar attack in Cambrils that left one woman dead and six people injured.
The identities of the other two dead jihadists are yet to be confirmed by police.
Four men, aged 21, 27, 28 and 34, who were arrested in connection with the attack remain in custody. Three are Moroccan and one Spanish, and police said none of them was previously known to the security services for terror-related reasons.
Moussa Oukabir’s older brother, Driss Oukabir, is reported to be one of those detained.
Some 34 nationalities were among almost 130 people wounded in the attacks in Las Ramblas and in Cambrils, which lies around 70 miles (110km) to the south-west.
Local authorities have identified six of the victims of the Barcelona attack as an Italian, one Portuguese, three Spanish and one Spanish-Argentine. The victim of the second assault in Cambrils has been identified as a Spanish woman.
Authorities said 54 people injured in the attacks were still in hospital on Friday night, with 12 in a critical condition and 25 in a serious condition.
Relatives of a seven-year-old who became separated from his mother during the Barcelona attack are continuing to appeal for information. The father and grandmother of Julian Alessandro Cadman are travelling to Spain from Australia as the wait for news continues, family member Debbie Cadman said.
Speaking after the family’s initial plea for help, the prime minister, Theresa May, said a child with dual British nationality was believed to be among those unaccounted for.
Four Australians were injured in the attack, the country’s foreign minister, Julie Bishop, said.
Canada’s prime minister Justin Trudeau said one Canadian was killed and four injured during the attacks.
Police have revealed that the terrorists behind the rampage were preparing bigger attacks, with an explosion on Wednesday at a house in Alcanar believed to have robbed the killers of materials to use in larger-scale operations.
Reports from Spain had earlier suggested the terror cell may have been planning an attack using gas canisters.
Police are also looking for a white Renault Kangoo vehicle which is believed to have been rented by the suspects and could have crossed the border into France, according to French media.
The attacks in Barcelona and Cambrils took place around eight hours apart on Thursday afternoon and in the early hours of Friday.
In an echo of the London Bridge attack in June, Catalonia president Carles Puigdemont said the five terrorists in the Cambrils car were wearing fake suicide belts when they were stopped. Police revealed that an axe and knives were also found in the vehicle, with one of the latter used to wound one person in the face before the terrorists were gunned down.
Ben Wallace, the UK security minister, said the terror threat to Britain was rising as Islamic State loses battles and territory in Syria and Iraq.
He told BBC Radio 4’s Today programme: “I think the threat is still increasing, partly driven by the fact Isis is collapsing in Syria and people are either unable to get out there to fight for Isis and so they look to do something at home, or also because people have come back and tried to inspire people with their stories and tales of the caliphate. I think those two things mean that the threat is to some extent increasing.”
Mr Wallace rejected suggestions that the government’s voluntary anti-radicalisation programme, Prevent, could be made compulsory. Simon Cole, the police lead for Prevent, had recently said that a debate was needed about introducing an element of compulsion for certain groups, such as returnees from Syria.
Meanwhile police in Finland have said a stabbing in the city of Turku on Friday was being investigated as murder with possible terrorist intent.