Three teams carried out the attacks in the French capital in which 129 people were killed and 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.
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 may 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.”
He also confirmed that one of the dead attackers had been identified as a 30-year-old Frenchman who had a criminal record but had never spent time in jail.
The man came from the town of Courcouronnes, 25km (15 miles) west of Paris. He had been identified by the security services as having been radicalised but had never been implicated in a counter-terrorism investigation.
Mr Molins said all seven militants had used Kalashnikov assault rifles and the same type of explosive vests.
On Saturday evening, a tourist thought he saw something suspicious at the Pullman hotel near the Eiffel Tower and sparked a security alert. But a police search found nothing and the operation was called off.
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 was 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 BBC’s 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.
A Syrian passport was found next to the body of one of three suicide bombers who struck near the Stade de France stadium during Friday’s game, Mr Molins confirmed.
A Greek minister says the passport belonged to a Syrian refugee who had passed through the island of Leros. 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.
A gunman opened fire on Le Carillon bar in the rue Alibert, near the Place de la Republique, before heading across the road to Le Petit Cambodge (Little Cambodia), killing a total of 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 in rue de la Fontaine au Roi, were also fired on, with the loss of five lives.
Mr Molins said 19 people had been killed at the Belle Equipe bar, 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.
La Belle Equipe, 92 rue de Charonne, 11th district – at least 19 dead in gun attacks
La Casa Nostra restaurant, 92 rue de la Fontaine au Roi, 11th district – at least 5 dead in gun attacks
Stade de France, St Denis, just north of Paris – explosions heard outside venue, three attackers dead
Bataclan concert venue, 50 Boulevard Voltaire, 11th district – stormed by four gunmen, at least 80 dead
Images of aftermath of shootings
#Paris: Power, horror, and lies
The 1,500-seat Bataclan concert hall 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 four attackers there were dead. Three had blown themselves up and a fourth was shot dead by police.
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 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.
West inevitable target: Frank Gardner, BBC security correspondent
From the moment that US-led coalition forces began to check the advance of IS’s rampage across Iraq in the summer of 2014, it was inevitable the West would become the militants’ target.
France is especially vulnerable. Its open borders have allowed easy access to the powerful automatic weapons used in all the Paris attacks this year.
At the same time, it has thousands of troops deployed overseas and it’s been confronting jihadists on three continents.
Its controversial ban on the burka face veil for women has been interpreted by some Muslims as being anti-Islamic.
But if IS is indeed behind this weekend’s carnage, then – taken with its claim of bringing down the Russian airliner over Sinai in October – it marks an alarming step-up in its global reach.
Largely because of the ongoing civil war in Syria, there remains a significant pool in Europe of returning jihadists, trained and inspired to carry out attacks in their own countries.
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