Explosions and gunshots were heard outside the building where a gunman had held at least five hostages. One woman was reportedly seen fleeing the Hyper Cacher market.
Reuters, however, reported that at least four hostages in the kosher grocery were dead, citing a police source.
The other hostage-taking ended Friday with a police raid, and the death of the two brothers suspected in the deadly shooting at the Charlie Hebdo newspaper offices in Paris on Wednesday.
Agence-France Press reported that special forces had removed the hostages after launching an assault at the store in the Porte de Vincennes area.
"We've got him," CNN reported a police officer as shouting. The newspaper Le Monde also reported the hostage-taker was killed.
The fate of the woman who was accompanying the gunman wasn't immediately clear.
Earlier, Paris police said Amedy Coulibaly and Hayat Boumeddiene were believed to be involved in the supermarket hostage-taking.
CBC's Nahlah Ayed, who is at the scene, reported hearing three explosions at the supermarket.
Earlier, according to a police official, the gunman inside the market threatened to kill hostages if police launched an assault on the other hostage scene north of the city, where the two brothers were cornered. The hostages in that incident were freed safely.
An official described the events as "clearly linked."
An official said several people had been wounded when the gunman opened fire in the market Friday afternoon and were able to flee and get medical care.
It wasn't clear whether other people were wounded inside the market, or whether the woman listed as the gunman's accomplice in a police bulletin was inside with him.
Earlier, a police official who was not authorized to speak about the situation said the man opened fire in the kosher market, near Paris's Porte de Vincennes, and declared, "You know who I am."
The armed man took hostages, police sources said, but they denied earlier reports that two people had been killed, Reuters reported.
The Paris mayor's office immediately announced the closure of all shops along Rosiers Street in the city's famed Marais neighbourhood in the heart of the tourist district.
Hours before the Jewish Sabbath, the street is usually crowded with shoppers — French Jews and tourists alike. The street is also only a kilometre away from Charlie Hebdo's offices.
Paris police released a photo of Amedy Coulibaly, 32, as a suspect in the killing Thursday of a policewoman, and the official named him as the man holed up in the market. He said the man is armed with an automatic rifle and some hostages have been gravely wounded.
He said a second suspect, a woman named Hayet Boumddiene, 26, is the gunman's accomplice.
Helmeted SWAT squads converged on the standoff.
The two men suspected in Wednesday's attack on the satirical newspaper had been on the run since gunning down 12 people.
France has been high alert for other attacks since the newspaper massacre.Suggest a correction