Two people have died during a police raid on a flat in Paris suburb Saint-Denis, while seven arrests were made.
A woman has blown herself up and a suspect was shot dead.
Police targeted the flat in Saint-Denis in a search for Abdelhamid Abaaoud, the alleged mastermind of last week’s attacks in Paris, when 129 people were killed.
The fate of Abdelhamid Abaaoud, previously thought to be in Syria, is still unclear.
A government spokesman said remains of a third body may be under the rubble.
Prosecutor Francois Molins announced earlier that intelligence indicated Abdelhamid Abaaoud was in Paris.
All victims of the attacks – which targeted a concert hall, cafes and the Stade de France stadium and were claimed by ISIS – have now been identified, the government said.
The operation in Saint-Denis – where the Stade de France is located – began at 04:20 local time.
Speaking from the scene afterwards, Francois Molins said it had been ordered after phone taps and surveillance operations suggested Abdelhamid Abaaoud, a Belgian of Moroccan descent, could be there.
The prosecutor said a young woman – said by France’s BFMTV to be a relative of Abdelhamid Abaaoud – had detonated her explosives belt soon after the raid began.
Another suspect was killed by grenades and police bullets, Francois Molins said.
The spokesman for the French interior ministry, Pierre-Henry Brandet, later told French TV station BFMTV that work was being done to establish whether the remains of a “third terrorist” were buried in the rubble.
Five members of the RAID police anti-terrorism unit were lightly injured while a RAID “assault dog”, a seven-year-old Belgian Shepherd called Diesel, was killed.
Three men were arrested in the apartment. Two others were found hiding in rubble and a further two – including the man who provided the lodging – were also detained, he said.
He did not give the identities of those detained.
As the operation got under way, roads were blocked off around Rue de la Republique in Saint-Denis, by truck-loads of soldiers and armed police.
Local residents, who were urged to stay indoors, spoke of hearing continuous gunshots and large explosions.
Amine Guizani told the Associated Press: “They were shooting for an hour, non-stop. There were grenades. It was going, stopping, Kalashnikovs, starting again.”
French Interior Minister Bernard Cazeneuve praised the security forces for operating “under fire for a number of hours in conditions that we have never seen before today”.
According to French chief prosecutor Francois Molins, three teams of attackers were involved in the Paris attack in which 129 people were killed and more than 350 wounded.
“We have to find out where they came from… and how they were financed,” he told reporters.
Francois Molins said seven attackers had been killed, and that all had been heavily armed and wearing explosive belts.
Last night’s attacks, claimed by ISIS, hit a concert hall, a major stadium, restaurants and bars.
Francois Molins also said the arrests of three men in Belgium on November 14 were linked to the attacks.
Belgian PM 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 November 14, Francois 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, 15 miles west of Paris. He had been identified by the security services as having been radicalized but had never been implicated in a counter-terrorism investigation.
Francois Molins said all seven militants had used Kalashnikov assault rifles and the same type of explosive vests.
He also gave details about the state of the investigation, which he said was at a very early stage.
The prosecutor 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 to a Frenchman living in Belgium who was identified in a spot check by police on Friday morning as he drove across the Belgian border with two others.
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, Francois Molins said.
A Greek minister says the passport belonged to a Syrian refugee who passed through the island of Leros. An Egyptian passport has also been linked to the attacks.
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 local time as people were enjoying a Friday night out in Paris.
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 15 people.
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.
Frnacois Molins said 19 people were killed at the Belle Equipe bar, while the toll from the attack on the Bataclan concert hall stood at 89.
At around 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 Francois Hollande was among the spectators and was whisked away after the first blast.
Investigators found the bodies of three suicide bombers around the Stade de France, Francois Molins said.
The 1,500-seat Bataclan concert hall suffered the worst of last night’s attacks. Gunmen opened fire on a sell-out gig by rock group Eagles of Death Metal, killing 89 people.
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.
ISIS released a statement on November 14 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 ISIS militants in Syria and Iraq.
Shortly before, President Francois 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 official 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.
According to a French prosecutor, the Thalys train attack on August 21 was premeditated and well prepared.
Moroccan Ayoub El-Khazzani, 25, was carrying 270 bullets for his assault rifle and a bottle of petrol, prosecutor Francois Molins told reporters on August 25.
The suspect’s phone showed that he had watched a jihadist video shortly before launching the attack, Francois Molins added.
Ayoub El-Khazzani was overpowered by passengers on the Thalys train. No-one died.
Three Americans and one Briton who tackled the gunman were awarded medals for their bravery.
“Ayoub El-Khazzani had watched YouTube audio files whilst already on the Thalys train in which an individual called on the faithful to fight and take up arms in the name of the Prophet [Muhammad],” Francois Molins told a news conference.
Francois Molins said a formal terrorism investigation had been opened, adding that other European authorities had passed on information about the suspect’s travels and links to radical Islam.