Three teams carried out the attacks in the French capital which killed 129 people and left more than 350 wounded, the Paris chief prosecutor says.
“We have to find out where they came from… and how they were financed,” Francois Molins told reporters.
He said seven attackers had been killed, and that all had been heavily armed and wearing explosive belts.
Friday’s attacks, claimed by Islamic State militants, hit a concert hall, a major stadium, restaurants and bars.
Prime Minister Manuel Valls has said France will continue with air strikes against IS in Syria and described the group as a very well-organised enemy.
Mr Molins confirmed that one of the dead attackers had been identified as a 29-year-old Frenchman who had a criminal record, but had never spent time in jail.
Omar Ismaïl Mostefai was identified after his finger was found at the Bataclan concert hall and matched fingerprints the police had on file, AFP reported.
Who were the victims?
Fear stalks Paris
Mostefai came from the town of Courcouronnes, 25km (15 miles) south of Paris. He had been identified by the security services as having been radicalised but had never been implicated in a counter-terrorism investigation.
Investigators are trying to find out whether he travelled to Syria in 2014, judicial sources told AFP.
French police have taken Mostefai’s father and brother into custody and searched their homes.
Mostefai’s older brother attended a police station voluntarily.
“It’s crazy, insane. I was in Paris myself last night, I saw what a mess it was,” he told AFP before being placed in custody.
He said he had not had contact with his younger brother for several years.
Mr Molins also said the arrests of three men in Belgium on Saturday were linked to the attacks.
Belgian Prime Minister Charles Michel said investigators were trying to establish whether one of the suspects picked up near Brussels might have been in Paris on Friday evening.
Speaking in Paris on Saturday evening, Mr Molins told reporters: “We can say at this stage of the investigation there were probably three co-ordinated teams of terrorists behind this barbaric act.”
Mr Molins said all seven militants had used Kalashnikov assault rifles and the same type of explosive vests.
Mr Molins also gave details about the state of the investigation, which he said was at a very early stage.
He said police were focusing on two vehicles. One is a black Seat used by gunmen at two of the attacks, and still untraced.
The other is a black Volkswagen Polo with Belgian registration plates found at the concert venue that was targeted.
He said this had been rented by a Frenchman living in Belgium.
He was identified while driving another vehicle in a spot check by police on Saturday morning as he crossed into Belgium with two passengers.
The Daily Released Hugh Schofield in Paris says investigators are working on the theory that these three may be another team of attackers who managed to flee the scene.
The Greek authorities say two people under investigation by the French police had registered in Greece as Syrian refugees. A Syrian passport was found near the body of one the attackers at the Stade de France.
An Egyptian passport has also been linked to the attacks.
How the attacks unfolded
French President Francois Hollande imposed a state of emergency after the worst peacetime attack in France since World War Two. It is also the deadliest in Europe since the 2004 Madrid bombings.
The violence began soon after 21:00 (20:00 GMT) as people were enjoying a Friday night out in the French capital.
Gunmen opened fire on Le Carillon bar and Le Petit Cambodge (Little Cambodia) restaurant, near the Place de la Republique in the 10th arrondissement (district), killing 15 people.
“We heard the sound of guns, 30-second bursts. It was endless,” resident Pierre Montfort said.
A few streets away, diners sitting on the terrace of La Casa Nostra pizzeria were also fired on, with the loss of five lives.
Mr Molins said 19 people had been killed at the Belle Equipe bar in the 11th arrondissement, while the toll from the attack on the Bataclan concert hall stood at 89.
At about the same time, on the northern outskirts of Paris, 80,000 people who had gathered to watch France play Germany at the Stade de France heard three explosions outside the stadium.
President Hollande was among the spectators and was whisked away after the first blast.
Investigators had found the bodies of three suicide bombers around the Stade de France, Mr Molins said. One other person died in the blasts.
La Belle Equipe, 92 rue de Charonne, 11th district – 19 dead in gun attacks
Le Carillon bar and Le Petit Cambodge restaurant at rue Alibert, 10th district – 15 dead in gun attacks
La Casa Nostra restaurant, 92 rue de la Fontaine au Roi, 11th district – five dead in gun attacks
Stade de France, St Denis, just north of Paris – explosions heard outside venue, three attackers and bystander dead
Bataclan concert venue, 50 Boulevard Voltaire, 11th district – 89 dead when stormed by gunmen
The 1,500-seat Bataclan concert hall in the 11th arrondissement suffered the worst of Friday night’s attacks. Gunmen opened fire on a sell-out gig by US rock group Eagles of Death Metal, killing 89 people.
“At first we thought it was part of the show but we quickly understood,” Pierre Janaszak, a radio presenter, told AFP news agency.
“They didn’t stop firing. There was blood everywhere, corpses everywhere. We heard screaming. Everyone was trying to flee.”
He said the gunmen took 20 hostages, and he heard one of them tell their captives: “It’s Hollande’s fault, he should not have intervened in Syria.”
Within an hour, security forces had stormed the concert hall and all three attackers there were dead.
Islamic State released a statement on Saturday saying “eight brothers wearing explosive belts and carrying assault rifles” had carried out the attacks on “carefully chosen” targets, and were a response to France’s involvement in the air strikes on IS militants in Syria and Iraq.
Shortly before, President Hollande said France had been “attacked in a cowardly shameful and violent way”.
“So France will be merciless in its response to the Daesh [Islamic State] militants,” he said, vowing to “use all means within the law.. on every battleground here and abroad together with our allies”.
Many officials buildings as well as Disneyland Paris have been closed, sports events have been cancelled and large gatherings have been banned for the next five days.