In an email sent to AFP, she also condemned "the horrendous murder in a similar manner of Samuel Paty two weeks ago", when the teacher was decapitated outside a school north of Paris, by an Islamist extremist, after he showed his pupils cartoons of the Prophet Mohammed during a lesson on freedom of speech.
French President Emmanuel Macron had following Paty's murder defended the cartoons and the right to mock religion, sparking widespread anger against in the Islamic world and several campaigns in Muslim-majority countries, including Turkey, to boycott French products.
Bachelet's office said she was deeply concerned that "inflammatory rhetoric from very different perspectives is feeding the social, religious and cultural divisions on which such violence thrives."
It lamented that such divisions, which lead to "hatred, violence and death, are being repeatedly stoked and re-stoked, in the name of religion as well as in the name of freedom of expression".
Bachelet insisted "we must stop this vicious cycle, before yet more lives are lost".
"Political and religious leaders, as well as the media, should not only avoid inciting violence, hostility or discrimination themselves, they should speak out firmly and promptly against hate speech," she insisted.
"They should also make it very clear that violence cannot be justified by prior provocation."
She also warned against blaming entire groups of people for the violent actions of individuals.
"Entire groups should never be stigmatised, or have their human rights violated in any way, because of such individual acts."