UN Secretary General Ban Ki-moon set the target during an annual event to encourage communities to abandon the practice.
Religious, traditional and local leaders met at UN headquarters to call for an end to female genital mutilation, or FGM.
Also known as female circumcision or cutting, the procedure poses a serious threat to the health and lives of young girls.
The UN's children's agency, UNICEF, says more than 200 million girls and women globally have suffered genital mutilation - far higher than previously estimated.
But Mr Ban says there is some progress being made.
"Since 2007, more than a dozen countries have enacted measures to tackle FGM. More than 950 legal cases have been prosecuted. And today, nearly all countries where it is prevalent outlaw the practice. We are working to extend that legal protection everywhere."
Ending female genital mutilation is part of a set of development goals adopted by UN member states last year.
Goal five counts among its targets eliminating FGM by 2030.
Ban Ki-Moon says new, unharmful rites of passage should replace female genital mutilation.
"Let us continue our campaign to empower these girls and so many others. Let us shift the focus away from mutilation to education. Let us make a world where FGM stands for Focus on Girls' Minds. How about this, FGM stands for Focus on Girls Minds."
The Secretary General gave an example of young girls in Kenya and Tanzania who spend a week away from their families to learn life skills instead of being cut.
The cutting ritual, practised in some African, Asian and Middle Eastern countries, usually involves the partial or total removal of a girl's external genitalia.
One survivor of the practice is Malian musician Inna Modja.
An emotional Ms Modja says she felt she lost part of her identity as a result of the procedure being performed on her at the age of four.
"When I was a teenager and I was on my path to become a woman, for me it was a very tough time. The path was really full of hurt and suffering because I had the physical pain and I also had the psychological pain. For me, not knowing who I was becoming because I felt that I would never become a woman because I had something missing and I wasn't worth it."
Another survivor, Keziah Bianca Oseko, says it's important that people continue to speak out against the ritual.
"I went through FGM when I was eight years old. And that to me is a scar that I have to stand with and to talk to people about it. So it's that that is in me. That's passion that is in me. That's pain that I went through. And I want to stand up and tell the world that FGM is not something that you need to talk about, but to end it, like right now."
