French President Francois Hollande declared Wednesday that Charlie Hebdo "is alive and will live on" after its new edition sold out in record time, as Al-Qaeda claimed the deadly attack on the satirical magazine.

"Today it is reborn," the president said of the magazine, after many Parisians joined long queues to get their hands on a copy which, true to controversial form, featured a cartoon of the Prophet Mohammed on its cover.

"You can murder men and women, but you can never kill their ideas," Hollande said.

The president is due Thursday to address the Arab World Institute in Paris, a cultural institute that promotes closer ties between France and the Arab world, while funerals will be held for two of the magazine's slain cartoonists.

The January 7 attack by Islamist gunmen at Charlie Hebdo's Paris offices left 12 people dead, including some of the country's best-loved cartoonists.

Debate is growing over where freedom of expression begins and ends, with millions rallying in support of free speech after the assault.

Meanwhile French prosecutors, under government orders to crack down on hate crimes, have opened more than 50 cases for condoning terrorism or making threats to carry out terrorist acts since the attack.

They include one against controversial comedian Dieudonne, who was arrested Wednesday over a remark suggesting he sympathised with one of the Paris attackers.

A 21-year-old in Toulouse was also sent to prison for 10 months on Monday under France's ultra-fast-track court system, for expressing support for the jihadists while travelling on a tram.

In Wednesday's new edition of Charlie Hebdo, the prophet is depicted with a tear in his eye, under the headline "All is forgiven", and holding a sign reading "Je suis Charlie" (I am Charlie), the slogan that has become a global rallying cry for those expressing sympathy for the victims and support for freedom of speech.

Around 700,000 copies were released and sold Wednesday as part of a print run that will eventually total five million -- dwarfing the usual 60,000 copies for a magazine that had long been threatened by a loss of readership.

Al-Qaeda's Yemen branch (AQAP) released a video Wednesday claiming responsibility for the attack, saying it was "vengeance" for the magazine's cartoons of the prophet.

Many Muslims consider images of Mohammed, not least ones satirising him, to be blasphemous under Islam.

"(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.

Brothers Said and Cherif Kouachi, who carried out the attack, are known to have trained with the group.

Amedy Coulibaly, who shot dead four Jews at a kosher supermarket in Paris and a policewoman the day before in attacks he said were coordinated with the Kouachi brothers, has claimed links to the Islamic State group in Syria and Iraq.

IS on Wednesday described Charlie Hebdo's decision to print another Mohammed cartoon as "extremely stupid".

New edition stirs anger in Islamic world

A Turkish court ordered a block on websites featuring Charlie Hebdo's defiant new cover, as anger grew in the Islamic world over the edition.

Cairo's Al-Azhar university, Sunni Islam's most prestigious centre of learning, warned that new Mohammed cartoons would only serve to "stir up hatred".

There were angry protests in the Philippines and Mauritania, while the Senegalese government said it was banning the dissemination of Wednesday's editions of Charlie Hebdo and the French daily Liberation, which also put a cartoon of the Mohammed on the front page.

But many have taken a nuanced stance and tried to calm tensions, with French Muslim leaders urging their communities -- which have been targeted with attacks on mosques in the wake of the shootings -- to "stay calm and avoid emotive reactions".

France has deployed armed police to protect synagogues and Jewish schools and called up 10,000 troops to guard against other attacks.

Prime Minister Manuel Valls admitted Tuesday that France's intelligence capabilities and anti-terrorism laws needed to be strengthened and "clear failings" addressed.

The three gunmen were known to French intelligence and on a US terror watch list "for years".

Belgian newspaper Het Laatste Nieuws reported that Coulibaly bought all their weapons -- including assault rifles and a rocket launcher -- near the Gare du Midi station in Brussels for less than 5,000 euros ($7,000).

Funerals for beloved cartoonists

Private family funerals will be held Thursday for renowned cartoonists Georges Wolinski, 80, and Bernard "Tignous" Verlhac, 57. Their colleague Jean "Cabu" Cabut, 76, was buried in the Champagne region on Wednesday.

British Prime Minister David Cameron and US President Barack Obama meanwhile vowed a united front against Islamic extremists in a joint editorial in The Times newspaper, published on the eve of a visit by Cameron to Washington.

"We will continue to stand together against those who threaten our values and our way of life," the two leaders wrote.

"When the freedoms that we treasure came under a brutal attack in Paris, the world responded with one voice."

Distributors quickly boosted Charlie Hebdo's planned print run from an initial three million to five million after Wednesday's sales rush. The commemorative issue will also be available in English, Spanish, Italian, Arabic and Turkish, with proceeds going to the victims' families.

The magazine, which last month did not have enough money to pay staff wages, could raise as much as 10 million euros in sales and donations since the attack.