(CNN) Al Qaeda in the Arabian Peninsula claimed responsibility Wednesday for last week's rampage that killed 12 people at France's Charlie Hebdo satirical magazine.

The attack was years in the making, an AQAP leader said in a video, claiming U.S.-born cleric Anwar al-Awlaki was the mastermind behind it.

Al-Awlaki was the terror group's spokesman before a U.S. drone strike killed him in Yemen in 2011. For days, intelligence analysts have been trying to piece together whether the gunmen who attacked the magazine met him on trips to Yemen -- a theory that could be bolstered by the new video's claim.

AQAP did not claim responsibility for Friday's deadly siege at a kosher grocery store in Paris, but praised it.

French security services have identified a suspected accomplice in that attack, according to the French newspaper Le Parisien . Police sources cited by the newspaper said one line of investigation is that the accomplice, a man from a Paris suburb, may have driven gunman Amedy Coulibaly to the kosher supermarket, where Coulibaly later shot dead four people.

Coulibaly was killed in a police raid to end the siege. Said and Cherif Kouachi, the brothers who authorities say were behind the Charlie Hebdo attack, also are dead. But investigators' efforts to track down possible suspects tied to last week's attacks are continuing.

So is the magazine that the terrorists targeted last week.

Charlie Hebdo's new edition hit newsstands Wednesday -- a week after authorities say terrorists Said and Cherif Kouachi burst into its newsroom and gunned down staffers.

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The cover features a cartoon of the Prophet Mohammed crying. All 3 million copies sold out quickly, but more copies are coming soon, the magazine said.

'Blessing from Allah'

The claim of responsibility for the deadly attack on the magazine came in a video showing AQAP commander Nasr Ibn Ali al-Ansi, with pictures of the Kouachis in the background.

"When the heroes were assigned, they accepted. They promised and fulfilled," al-Ansi said.

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He praised the attack, saying it was revenge for Charlie Hebdo's depictions of Mohammed.

Al-Ansi blamed not only Charlie Hebdo, but also France and the United States.

"It is France that has shared all of America's crimes," al-Ansi added. "It is France that has committed crimes in Mali and the Islamic Maghreb. It is France that supports the annihilation of Muslims in Central Africa in the name of race cleansing." ("Islamic Maghreb" refers to North Africa.)

"It was a blessing from Allah" that the kosher market siege, in which four hostages were killed, took place about the same time, al-Ansi said.

Official: Video is authentic but not sure about claim

U.S. authorities said they think the video is authentic. But they weren't ready to say that AQAP helped carry out the assault.

"We're not there yet. There are good indicators" that the group was behind the attack, but the intelligence community is still assessing, a senior administration official told CNN.

Earlier in the day, U.S. National Security Council spokesman Alistair Baskey said that, "if genuine, this is only the latest example of the wanton brutality that is al Qaeda's calling card and which it has visited upon innocents of all faiths."

Investigators believe Cherif Kouachi left Yemen with as much as $20,000 from AQAP to carry out attacks, a U.S. official said.

Report: Raid pointed to new suspect

Le Parisien's report said investigators identified Coulibaly's suspected accomplice using keys for a motorbike discovered in an apartment they raided over the weekend.

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Also found inside the apartment, according to Le Parisien: a stash of weapons, explosives and two ISIS flags.

Coulibaly purportedly told authorities before he was killed that he belonged to ISIS

Police also suspect the man may have been responsible for shooting and wounding a jogger last week -- an attack that the Paris prosecutor has said could be tied to Coulibaly because the ammunition used was the same as ammunition found at the scene of the kosher market attack, Le Parisien said.

Paris police would not comment to CNN on the contents of the report.

Le Parisien says Coulibaly's accomplice, who the newspaper did not name, is suspected to have fled France, possibly for Syria.

Officials have also said they believe Hayat Boumeddiene, Coulibaly's widow who may have played a role in the attacks, has fled to Syria.

More terror cases

With France on its highest level of alert, 10,000 troops have deployed across the country. Thousands of police officers are on patrol, including hundreds assigned to protect Jewish schools.

Since the attacks, dozens of cases have been opened in France against people accused of expressing support for terrorism since the attacks, the Justice Ministry said.

It's unclear how many people are blamed for the 54 infractions. The cases include investigations involving phone threats, cyberattacks and Facebook posts, the ministry said.

Some are in prison awaiting trial, some have already been convicted, and some have been released with a notice of a court date, ministry spokesman Pierre Rance said.

Penalties for the alleged crimes vary, Rance said.

Justice Minister Christiane Taubira "considers that words or actions of a racist or anti-Semitic nature, or that cause hateful, violent, or discriminatory behavior, or advocate terrorism, or target security forces must be fought and pursued with the utmost vigor," her office said in a statement.

She "asked prosecutors to exercise extreme reactivity in the conduct of public action against the perpetrators of such crimes," the statement said.

French comedian arrested

With concerns on the rise, a controversial French comedian was accused of publicly supporting terrorism, French media reported.

Dieudonne M'bala M'bala, known as Dieudonne, was arrested in Paris, according to media reports, which tied his arrest to a recent Facebook post from the comedian. "Je suis Charlie Coulibaly," the post said, combined the last name of one of the terrorists involved in last week's attacks with the widely used phrase expressing solidarity with victims

That post has since been deleted.

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On Monday, Dieudonne issued a statement with his stance on the terror attacks.

"Since the beginning of last year, I have been treated as public enemy number one, when all I try to do is make people laugh, and laugh about death," he wrote in a letter to the French interior minister. "Because death laughs at us all, as Charlie knows now, unfortunately."