But in an interview with France's Le Journal du Dimanche on Sunday, the hacker also said he was against violence and did not support those who are suspected of having firebombed the weekly's offices.
The Paris offices of the weekly, Charlie Hebdo, were destroyed in a fire on Wednesday after it published a special Arab Spring edition with Mohammed on the cover as "guest editor" saying: "100 lashes if you don't die of laughter!"
Police said they suspect the offices were firebombed and the newspaper has said it received threats from Muslim fundamentalists.
The weekly's website was also taken down in a cyber-attack claimed by Turkish hackers' group Akincilar. It remained offline on Sunday.
"We didn't do anything wrong, it's not like we siphoned off bank accounts. This was a protest against an insult to our values and beliefs," the hacker, who identified himself as Ekber, told the newspaper in Istanbul.
The 20-year-old, who uses the hacker name Black Apple, said he had launched the attack after reports broke online of the weekly's plans. He said it took six hours of work by a team of hackers to take down into the site.
However, when asked whether he supported the firebombing, Ekber said: "Of course not, we do not support violence. Islam is a religion of peace."
He said the group was also prepared to launch cyber-attacks on another French newspaper, Liberation, which has republished the images.
Charlie Hebdo has said its site remains offline because the Belgian company hosting it, Bluevision, was refusing to reinstate the page after receiving death threats.
It has also claimed that Facebook threatened to terminate its account because it was publishing inappropriate images.
Akincilar, the Turkish hackers' group, is named after the famed Akinci warrior-horsemen of the Ottoman Empire and has claimed responsibility for thousands of cyber-attacks in recent years.
The group has previously targeted the site of a Turkish satirical magazine, The Penguin, after it questioned Islamic faith in a cartoon.
It has also carried out attacks on Israeli, Armenian and Kurdish websites in what it said was the defence of Turkish national values.