Satire magazine Charlie Hebdo made a defiant return on Wednesday with a new issue that sold out across France in record time, as Al-Qaeda posted a video claiming last week's deadly attack on its cartoonists.

The satirical magazine once again featured Mohammed on its cover - but with a tear in his eye, holding a "Je Suis Charlie" (I am Charlie) sign under the headline "All is forgiven."

Many Parisians joined long queues outside newspaper kiosks in the pre-dawn cold to get their hands on one of 700,000 copies released in a run that will eventually total five million.

"This issue is symbolic, it represents their persistence, they didn't yield in the face of terror," said Catherine Boniface, a 58-year-old doctor, disappointed to have come up empty-handed at one Paris newsstand.

Al-Qaeda's Yemen branch (AQAP) claimed responsibility for the attack by Islamist terrorists on the Paris offices of the weekly last Wednesday, that left 12 people dead including the country's best-loved cartoonists.

"(AQAP) was the party that chose the target and plotted and financed the plan. ...It was following orders by our general chief Ayman al-Zawahiri," said one of its leaders in the video, adding it was "vengeance" for the weekly's cartoons of Mohammed.

Brothers Said and Cherif Kouachi who carried out the Charlie Hebdo attack are known to have trained with the group. Amedy Coulibaly, who killed a policewoman and attacked the Hyper Cacher kosher supermarket on Friday in attacks he said were coordinated with the Kouachi brothers, has claimed links to the Islamic State (ISIS) group in Syria and Iraq.

ISIS on Wednesday described Charlie Hebdo's decision to print another Mohammed cartoon as "extremely stupid.” The Grand Mufti of Jerusalem Mohammed Hussein, himself a sympathizer of the Islamist terrorist movement, said the cover was an insult that "has hurt the feelings of nearly two billion Muslims all over the world."

Meanwhile, the French government said Wednesday it had instructed prosecutors to get tough on people who condone terrorism or carry out racist and anti-Semitic attacks.

Over 50 cases for condoning terrorism have been opened since the attacks that claimed 17 lives, including the arrest on Wednesday of controversial comedian Dieudonne Mbala Mbala.

He wrote "I feel like Charlie Coulibaly" on Facebook on Sunday – mixing the popular "Je Suis Charlie" homage to the slain journalists with a reference to the supermarket gunman who murdered four Jews. Under France's ultra-fast-track court system, a 21-year-old in Toulouse was sent to prison for 10 months on Monday for expressing support for the jihadists while travelling on a tram.

French Prime Minister Manuel Valls said Tuesday the country was now engaged in a "war on terrorism," in remarks reminiscent of former US president George W. Bush after the 9/11 attacks in 2001.

But Valls stressed that Muslims would always have a home in France, saying "I don't want Jews in this country to be scared, or Muslims to be ashamed of their faith."