Long queues have formed at newsstands in France for the latest edition of satirical magazine Charlie Hebdo.
Five million copies are being printed - a week after Islamist gunmen murdered 12 people at its offices and five others in subsequent attacks in Paris.
The cover shows a cartoon depicting the Prophet Muhammad weeping while holding a sign saying "I am Charlie".
Al-Qaeda in Yemen claimed the attack on the magazine in a video purportedly from the group.
It is believed earlier cartoons of the Prophet prompted the attack on the magazine.
"I am Charlie" emerged as a message of support for the magazine following the attack on 7 January, which left eight journalists, including its editor, dead in addition to four others.
In a separate attack in Paris two days later, four Jewish men died after an Islamist gunmen took hostages at a kosher shop in the French capital.
A police woman was shot dead in a third shooting believed to have been carried out by the same attacker.
Three million copies of the latest edition of Charlie Hebdo were originally printed for distribution.
Copies in France quickly sold out on Wednesday morning. Editors then decided to increase the print run to five million. Normally, only 60,000 are printed each week.
Demand for what is being called the "survivors' issue" of the magazine is high, in part because the proceeds will go to the victims' families, correspondents say.
Kiosk owners told French media they had received large numbers of reservation requests, while at one shop in Paris all copies were reportedly sold out within five minutes.
Charlie Hebdo's decision to publish another cartoon of the Prophet has already generated threats from militant Islamist websites and criticism from the Islamic world, the BBC's Chris Morris in Paris reports.
The self-styled Islamic State (IS) militant group said on its radio station that the publication of the cartoon was "an extremely stupid act".
Meanwhile, a new video said to be from al-Qaeda in Yemen (AQAP) was aired on Wednesday saying the group was behind last week's attack on the magazine.
The group "chose the target, laid the plan and financed the operation", which was conducted in "vengeance for the prophet", the video message said.
It added that it was a "success" that the Charlie Hebdo attack "coincided" with the attacks by supermarket gunman Amedy Coulibaly.
Coulibaly had pledged allegiance to IS in a video message, while the Charlie Hebdo attackers, Said and Cherif Kopuachi, had said they were acting on behalf of AQAP.
Coulibaly had also said they had co-ordinated the attacks, but experts say it is highly unlikely IS and AQAP, rivals in the Middle East, would plan an attack together.
Hugh Schofield in Paris on the new edition:
There's the full-page cartoon of a weeping Muhammad on the front cover, but inside there are no more caricatures of the Prophet.
There are plenty - in the paper's characteristic scurrilous vein - of Muslim extremists. In one cartoon, two terrorists are seen ascending to heaven and asking: "Where are the 70 virgins?" In the background, the murdered staff at Charlie Hebdo are enjoying an orgy.
An editorial thanks the millions of people who have declared themselves as Charlie in the past few days - but it says it wants no more of the past insinuations that by provoking Muslims, it has somehow brought trouble on itself.
The issue will be available in six languages - including English, Arabic and Turkish - some in print and some online.
Turkish newspaper Cumhuriyet has published a section of the magazine, including a small image of the cover. It had originally planned to publish the full edition, but scaled down its plans due to security concerns.
Very few outlets in the Middle East and North Africa have shown the image.
Referring to last week's shocking events, French Prime Minister Manuel Valls said his country was at war with extremism and terrorism - but not with Muslims.
He was speaking on Tuesday after funeral ceremonies were held for seven of the victims in France and Israel.
France has deployed 10,000 troops at various sites across the country - including synagogues, mosques and airports - in response to the attacks.
Meanwhile, controversial French comedian Dieudonne M'bala M'bala was arrested on Wednesday for "defending terrorism".
Police opened an investigation into the comic on Monday, after he wrote on a Facebook post "I feel like Charlie Coulibaly" - merging Charlie Hebdo with the name of supermarket gunman Amedy Coulibaly.
Suspect on the run
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New mobile phone footage shows the Kouachi brothers opening fire on police
The brothers were later killed by French security services after a stand-off in a town north of Paris.
Separately, Coulibaly - whom investigators have linked to the brothers - killed the four men at the kosher supermarket on Friday, apparently before police stormed the building. Coulibaly is also believed to have shot dead the policewoman the day before.
His partner Hayat Boumeddiene is now thought to be in Syria. She has been identified as a suspect by French police, although she left France before the attacks.