Claiming responsibility for the assault on Paris, the Islamic State jihadist group has said the Friday's attacks are just the "beginning of the storm".

Its propaganda arm released statements in Arabic and French claiming the "blessed battle" was an act of revenge for France's involvement in the US-led coalition bombing its militants in Iraq and Syria.

An audio message was also released in English of the same statement, read by a supporter speaking with an American accent.

"A group of believers from the soldiers of the Caliphate set out targeting the capital of prostitution and vice, the lead carrier of the cross in Europe, Paris," he said.

"They divorced worldly life and advanced towards their enemy hoping to killed for Allah's sake…and his allies.

"Allah granted victory upon their hands and cast terror into the hearts of the crusaders in their very own homeland."

Isis' statement said eight "brothers" were armed with assault rifles and wearing explosives belts that they detonated when their ammunition ran out.

Saying the targets were "precisely chosen", the group described the sold-out Eagles of Death Metal gig where the majority of victims were shot dead as the "hundreds of pagans gathered for a concert of prostitution and vice".

Isis noted Francois Hollande's presence in the Stade de France for the football match between Germany and France, where two suicide bombers detonated their vests.

The statement continued: "Let France and all nations following its path know that they will continue to be at the top of the target list for the Islamic State and that the scent of death will not leave their nostrils as long as they partake part in the crusader campaign…and boast about their war against Islam in France, and their strikes against Muslims in the lands of the Caliphate with their jets.

"This is just the beginning of the storm."

The statement contained several inaccuracies, claiming that 200 people were killed and listing shootings in the 18th arrondissement, where there was no attack.

Isis also released an undated video yesterday threatening to attack France if it continued intervention in Iraq and Syria.

"As long as you keep bombing you will not live in peace. You will even fear traveling to the market," said one of the militants, identified as "Abu Maryam the Frenchman".

The militants, who appeared to be French citizens, sat cross-legged in a group wearing military fatigues and brandishing guns, while burning passports.

"You have been ordered to fight the infidel wherever you find him - what are you waiting for? There are weapons and cars available and targets ready to be hit," said Abu Maryam.

Another militant, identified as "Abu Salman the Frenchman", said: "Even poison is available, so poison the water and food of at least one of the enemies of Allah.

"Terrorise them and do not allow them to sleep due to fear and horror."

French President Francois Hollande said on Saturday the attacks in Paris were "an act of war" organised by Isis militants abroad with internal help.

He said the French army and security forces were mobilised "at the highest possible level" and insisted France would "triumph over barbarity".

"What we are defending is our country, but more than that, it is our values," he added.