The attacks were designed to show France would remain a top target for the jihadist group as long as the country continued its current policies, the group said in a statement.
Gunmen and bombers killed at least 127 people in Friday’s attacks.
Islamic State earlier on Saturday distributed an undated video threatening to attack France if bombings of its fighters continued.
The group’s foreign media arm, Al-Hayat Media Centre, made threats through several militants who called on French Muslims to carry out attacks.
“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 location of the Islamic State fighters in the video was not clear and it was not possible to determine when it was filmed, but the message was unmistakable.
The militants, who appeared to be French citizens, sat cross-legged in a group wearing fatigues and holding weapons in what appeared to be a wooded area.
The video showed the militants burning passports.
“Indeed 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.”
“Terrorize them and do not allow them to sleep due to fear and horror,” he added.
Foreign fighters who join Islamic State, the group which controls large swathes of Iraq and Syria, are seen as especially dangerous because Western passports enable them to live in and travel to Western countries undetected.
“Act of war”
Earlier the French President, Francois Hollande said that the attacks by IS were “an act of war”.
The multiple attacks across the city late on Friday were “an act of war… committed by a terrorist army, the Islamic State, against France, against… what we are, a free country,” he said.
French President declared three days of national mourning following the deadly Paris attacks.
He called the three-day observance after what he called acts of “absolute barbarity” late Friday that killed at least 128 people and wounded more than 200 others, many of them seriously.
Earlier, France’s foreign minister said the Paris attacks show it is more vital than ever to coordinate global efforts to fight terrorism, vowing that French “international action” will not stop.
“It is more necessary than ever in the current circumstances to coordinate the international fight against terrorism,” Laurent Fabius said in Vienna at talks on ending the Syrian civil war.
“And one of the aims of the meeting today in Vienna is exactly to see concretely how we can further increase the international coordination in the struggle against Daesh,” Fabius told reporters, referring to the Islamic State jihadist group which has overrun swathes of Syria and Iraq.
He added that in spite of the attacks “international action by France will continue.”