"It is still a possibility but, unlike four hours ago, it is losing weight", he told regional TV.
Thirteen people died and more than 100 were injured when a van drove into pedestrians on the crowded Las Ramblas street, an incident that local police are treating as an act of terrorism.
Spanish media have said Abouyaaqoub was suspected of being the driver, who fled after the attack.
Spain's deadliest terrorist attacks in more than a decade showed how a tourist hotspot can also be a hub for Islamic militants.
He was one of three suspects still being hunted Saturday, one of whom was identified by police as Moroccan-born Younes Abouyaaqoub, 22, from Ripoll, a town northwest of Barcelona.
The five assailants had an axe and knives in their auto and wore fake explosive belts, police said.
Police say they have arrested four men suspected of having a role in the attacks.
In the wake of the horrific terror attacks in Spain this week, it has been revealed that things could have been much worse for the people of Barcelona and Cambrils as explosives were found in a house in Alcanar.
The apparently accidental explosion at the house forced the suspects to scale down their plans and carry out more "rudimentary" attacks. "Soon after, loads of cars, bikes and ambulances arrived and then the armed police".
ISIS claimed responsibility for the carnage in Barcelona.
Previous year police recommended installing barriers or bollards along Las Ramblas to protect people from attacks by vehicles.
The attacks left 13 people dead in Barcelona and one woman dead in Cambrils.
"Our hearts and prayers go out to the families and loved ones of the innocent victims who perished and those who got injured in Barcelona", Palace spokesman Ernesto Abella Abella said.
Amid heavy security, Barcelona tried to move forward Friday, with its iconic Las Ramblas promenade quietly reopening to the public and King Felipe VI and Prime Minister Mariano Rajoy joining thousands of residents and visitors in observing a minute of silence in the city's main square.
The ministry expressed condolences to the families of the victims and injured and to the Spanish people and government.
Nunes told KGO she was separated from Tucker during the attack in Barcelona's Las Ramblas district on Thursday evening. "Terrorism is the biggest menace humanity is facing today with all pluralist and open societies increasingly encountering new levels of threat".
Vancouver police said Sunday that 53-year-old Canadian Ian Moore Wilson was among those killed in Barcelona and his wife Valerie was wounded.