Amedy Coulibaly, 32, shot a policewoman on Thursday, before attacking the supermarket on Friday, where he opened fire, killing four people before taking hostages. He was killed during the police assault.

Le Monde reported that in the video, which has now been taken down, Coulibaly claims to have coordinated his attack "against police" with the attack against satirical newspaper Charlie Hebdo by brothers Said and Cherif Kouachi, who killed 12 people.

He boasts of belonging to IS, also known as ISIS or ISIL, and says the organization gave money to the Kouachi brothers to buy weapons and other equipment, the paper added.

Le Monde said it received confirmation that the man in the video was Coulibaly from his former lawyer, Damien Brossier. It is not known when it was shot.

French television channel BFMTV reached Coulibaly before the standoffs ended, and he told the broadcaster he was with the ISIS group, and that he "coordinated" with the Kouachis.

Coulibaly is also linked to the shooting of a jogger on the same day as the Charlie Hebdo massacre, a prosecutor said Sunday.

In a brief statement, the prosecutor said ballistics tests on shell cases from the shooting Wednesday in Fontenay aux Roses linked them to the automatic weapon at the kosher store stormed by Coulibaly, two days later. The prosecutor said the jogger was seriously wounded.

In the video, apparently filmed over several days, Coulibaly can be seen with a gun, exercising and giving speeches in fluent French and broken Arabic in front of an IS emblem. He defends the attacks carried out on Charlie Hebdo, police and the supermarket.

The seven-minute video opens with Coulibaly working out and doing press-ups, followed by text describing him as a "soldier of the caliphate" and the "author" of an attack in Montrouge - during which a police officer was killed on Thursday.

"What we are doing is completely legitimate, given what they are doing," Coulibaly tells the camera."You cannot attack and not expect retribution so you are playing the victim as if you don't understand what's happening."

The SITE Intelligence Group said it had verified the video, which it said was released by a terrorist linked to IS.

A former drug dealing associate of Coulibaly's confirmed to The Associated Press that the man in the video was the slain gunman He spoke on condition of anonymity because he did not want to attract police attention.

Coulibaly's widow, who has been named as an accomplice, is believed to have traveled to a Turkish city near the Syrian border and then all traces of her were lost, according to a Turkish intelligence official, who was not authorized to speak on the record.