Paris supermarket gunman Amedy Coulibaly linked to third shooting by ballistics evidence

Police say man who took over kosher supermarket and killed a female police officer also shot a jogger

Amedy Coulibaly, who was shot and killed by police after he stormed a Kosher supermarket in Paris and took multiple hostages, killing four (AP)

Paris police have linked the gunman who took over a kosher supermarket and shot dead a female police officer with a third shooting on the day of the Charlie Hebdo massacre.

Amedy Coulibaly killed a policewoman on the outskirts of Paris the day after Said and Cherif Kouachi shot dead 10 journalists and two police officers at the magazine's offices.

He went on to take at least a dozen hostages at a supermarket, killing four people, before police shot him and the Kouachi brothers in near-simultaneous siege operations.

The jogger was left seriously wounded in the incident, which went largely overlooked as the world's attention focused on events at Charlie Hebdo.

Earlier on Sunday, a video emerged in which Coulibaly can be seen pledging allegiance to the Isis militant group.

Filmed by Coulibaly at times when he was on the run between shootings, it defends the Paris attacks as "retribution" for Palestinians in Gaza and Muslims in Afghanistan, Iraq and Syria.

Coulibaly also claims that the attacks were coordinated by himself and the brothers as "a team" - despite Cherif Kouachi's own suggestion before he died that he and Said Kouachi were working for al-Qaeda in Yemen.

Meanwhile, five people detained in connection with the three days of bloodshed in France have been released from custody, the prosecutor's spokesperson said.

Family members of the attackers have been given preliminary charges, but Agnes Thibault-Lecuivre said no one remained in detention over the attacks that left 17 people dead.