"The mutilation of girls and women must stop in this generation, our generation," UN Secretary General said on a visit to the Kenyan capital Nairobi.
"Men and boys must also be encouraged to support the fight against FGM -- and they should be praised when they do."
FGM ranges from the hacking off of the clitoris to the mutilation and removal of the entire female genitalia, and is carried out from the youngest babies to teenagers.
Communities originally from those countries have also carried the painful tradition to Western nations.
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"It is not culture, it is a violation of human rights," FGM survivor Kakenya Ntaiya said at the launch of the campaign.
"Girls' dreams, their hopes, their lives are being shattered."
Apart from the intense pain itself, immediate dangers include bleeding and infection.
In the longer term, risks include infertility and complications during childbirth, sometimes resulting in the death of the baby.
Ntaiya, a 36-year-old Kenyan mother of two, described the intense pain and damage caused when she was cut as a young girl, still a common practice for the Maasai people she comes from.
"It was devastating undergoing the cut, it was horrible and very painful," she told AFP. "I would never wish for any young girl to undergo that."
Campaigners call the dangerous practice mutilation rather than the term female circumcision, so as to make clear the dangers it involves and harm it causes.