Four hostages have been killed at HyperCacher as anti-terror forces stormed the Jewish supermarket in eastern Paris.
Several hostages were being held by a gunman with links to Charlie Hebdo attack suspects.
It is not clear whether the four hostages were killed before or after the police assault began.
Another four hostages were seriously injured, but 15 were freed alive.
After the police operation started, several hostages could be seen leaving the HyperCacher supermarket.
Two police officers were injured in the rescue operation, AP reported.
In a separate incident, a hostage at the warehouse in Dammartin-en-Goele, 22 miles north of Paris was also freed, while a police officer at the scene was injured, AFP news agency said.
Charlie Hebdo attack suspects Cherif and Said Kouachi have been killed in the incident.
French President Francois Hollande has described the events as “a tragedy for the nation”.
In a national address, Francois Hollande thanked the security forces for their “courage, bravery [and] efficiency”, but added that France still faced threats.
“We have to be vigilant. I also ask you to be united – it’s our best weapon,” he said.
“We must be implacable towards racism,” he added, saying that the supermarket attack was an “appalling anti-Semitic act”.
“Those who committed these acts, these fanatics, have nothing to do with the Muslim faith.”
The police assaults came after three tense days in France.
Twelve people were shot dead and 11 were injured in Wednesday’s attack on the office of Charlie Hebdo magazine.
The unprecedented attack shocked France and there has been an outpouring of sympathy and solidarity worldwide.
The two suspects of the Charlie Hebdo shootings, brothers Cherif and Said Kouachi, then went on the run for two days, before being surrounded at Dammartin as night fell on Friday.
French police said they came out firing.
The hostage taker in eastern Paris targeted Jewish supermarket HyperCacher, near Porte de Vincennes. He has been named as Amedy Coulibaly, 32. It is not clear whether he had an accomplice.
He knew at least one of the suspected Charlie Hebdo attackers, a source told AFP news agency.
Amedy Coulibaly had threatened to kill his captives if police attempted to capture the brothers, reports citing police said.
Earlier on Friday, a man claiming to be Amedy Coulibaly told French TV station BFMTV that he was a member of the Islamic State militant group, and that he had “co-ordinated” his attack with the Kouachi brothers.
Amedy Coulibaly was also suspected of being behind the shooting of a policewoman in the southern suburb of Montrouge on January 8.
On January 9, French police issued an appeal for witnesses to that shooting. They said they were looking for Amedy Coulibaly, as well as a woman called Hayat Boumeddiene, 26.
Hayat Boumeddiene’s whereabouts are not clear.
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Police have stormed two hostage sites in Paris and north of the city.
Gunshots and explosions have been heard at a printing facility in Dammartin-en-Goele, where two suspects in the Charlie Hebdo shootings, Cherif and Said Kouachi, were holding at least one hostage.
French media are reporting that brothers Cherif and Said Kouachi have been killed.
Explosions and gunfire could also be heard at kosher supermarket HyperCacher in eastern Paris, at Porte de Vincennes.
A gunman there was thought to be holding several hostages. Reports suggest he is linked to the Charlie Hebdo suspects.
Several hostages could be seen coming out from the HyperCacher supermarket.
The hostage at the printworks warehouse has also been freed, AFP news agency said.
Heavily armed anti-terror teams are mobilized in eastern Paris after a gunman has seized hostages at a kosher supermarket.
Schools near the supermarket are under lockdown, AP news agency reports.
Separately police have ordered the closure of all shops in the Marais, a traditionally Jewish area in the heart of Paris’s central tourist district.
The hostage-taker in eastern Paris – said to have taken up to five people prisoner – knew at least one of the suspected Charlie Hebdo attackers, a source told AFP news agency.
The gunman is suspected to be behind the shooting of a policewoman in Montrouge on January 8.
French police have issued an appeal for witnesses to that shooting. They said they were looking for two people: a man called Amedy Coulibaly, 32, and a woman called Hayat Boumeddiene, 26.
The two were thought to be “armed and dangerous”, French police said.
The Charlie Hebdo attackers, named as brothers Said and Cherif Kouachi, linked by intelligence officials to militant groups, shouted Islamist slogans during the shooting at the magazine office on January 7 and then fled Paris in a hijacked car, heading north.
Shots were fired during a high-speed car chase earlier on Friday.
It appears the suspects had hijacked another car in the town of Montagny-Sainte-Felicite before travelling on to Dammartin.
The car’s owner is said to have recognized them as brothers Cherif and Said Kouachi, the key suspects.
In a televised statement, Interior Minister Bernard Cazeneuve confirmed the men being sought on January 9 were those wanted for the Charlie Hebdo attack and said they would be “neutralized”.
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Hostages have been taken by a gunman at a Jewish bakery at Porte de Vincennes in Paris.
There are suggestions that the gunman may be the one who shot dead a female police officer on January 8. Police are now evacuating the area.
Separately, an intense standoff is ongoing between police and the Kouachi brothers suspected of carrying out the massacre at satirical magazine Charlie Hebdo, on January 7.
The gunman, believed to be the same man who killed a policewoman in Montrouge, southern Paris, on January 8 has reportedly stormed a kosher bakery and grocery store in the Vincennes area, taking five people hostage.
Witnesses said the man is heavily armed and opened fire upon entering the premises. Early reports suggest at least one person was injured in the shooting.
Security forces have rushed to the scene and are cordoning off the area.
The hostages are said to include women and children. Vincennes is located on the eastern outskirts of Paris.
Earlier local media named the Montrouge gunman as Amedy C., a 32-year-old radical belonging to the same jihadi cell of Cherif and Said Kouachi, the brothers who allegedly responsible for the Charlie Hebdo massacre.