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"As for the blessed Battle of Paris, we, the Organisation of al Qaeda al Jihad in the Arabian Peninsula, claim responsibility for this operation as vengeance for the Messenger of God," said Nasser bin Ali al-Ansi, a leader of the Yemeni branch of al Qaeda (AQAP) in the recording.
Gunmen killed a total of 17 people in three days of violence that began when they opened fire at Charlie Hebdo in revenge for its past publication of satirical images of the Prophet.
Ansi, the main ideologue for AQAP, said the "one who chose the target, laid the plan and financed the operation is the leadership of the organization", without naming an individual.
Brothers named Said and Cherif Kourachi claimed that they carried out the Charlie Hebdo attack. Said spent time in Yemen in 2011, and The New York Times reported that Said trained for "a few months" on small arms with AQAP.
CBS reported that Said Kouachi returned from Yemen in 2011 with $20,000 from AQAP to finance the operation in Paris. French police say the weapons also came from abroad.
On Jan. 7, gunmen attacked the magazine Paris offices, killing 12 people including several members of the magazine's staff.
Two days later, police killed the two brothers suspected of carrying out the massacre. Also on Jan. 9, a suspected accomplice of the brothers killed four people at a kosher grocery store in Paris before police stormed the building and killed the suspect.
A suspected partner of that man has now fled to Syria.
French police
AQAP is considered to be one of al-Qaeda's most dangerous offshoots. The Charlie Hebdo strike is the Yemen-based branch's first successful strike outside its territory.
AQAP itself is led by Nasser al-Wuhayshi, who is also Zawahri's number two in the network's global hierarchy.
"We did it in compliance with the command of Allah and supporting His Messenger, peace be upon Him," Ansi added.
It was not immediately possible to verify the authenticity of the recording, which carried the logo of the al Qaeda's media group al-Malahem.
Charlie Hebdo angered Islamic militant groups by regularly publishing cartoons and articles that lampooned jihadists including caricatures of the prophet Muhammad, which many Muslims find offensive. The magazine's offices were firebombed in 2011.
The first edition of Charlie Hebdo published after last week's attacks sold out within minutes at newspaper kiosks around France on Wednesday, with people queuing up to buy copies to support the satirical weekly.
(Reporting by Sami Aboudi and Yara Bayoumy, Editing by William Maclean and Dominic Evans)