David Cameron has said female genital mutilation (FGM) and childhood forced marriage should be stopped worldwide "within this generation".
Speaking at a global summit in London, the prime minister said Britain had no "special magic" to stop the practices – so global action was needed.
Mr Cameron has also unveiled a range of measures to tackle FGM in the UK.
As part of this, parents in England and Wales will face prosecution if they fail to stop daughters undergoing FGM.
Mr Cameron told the Girl Summit the existence of the practices were "standing rebukes to our world".
"It is absolutely clear about what we are trying to achieve," he said.
"It is such a simple but noble and good ambition and that is to outlaw the practices of female genital mutilation, and childhood and early forced marriage, to outlaw them everywhere for everyone within this generation."
He said the summit was intended to use the "power of convening people to come up with ideas and commitments to outlaw these practices".
Hosted by the UK government and children's charity Unicef, the summit is being attended by international politicians, campaigners including the Pakistani teenager Malala Yousafzai, and women who have undergone FGM.
The summit is also looking at ways to end forced marriage.
Phumzile Mlambo-Ngcuka, executive director of UN Women, said the situation was improving but many girls remained at risk.
"The fact that 30 million girls are at risk of being cut in the coming years clearly means that we have a big challenge on our hands," she said.
Priscilla Karim, who was forced to undergo FGM in Sierra Leone aged nine, described her ordeal.
She said: "I felt the worst pain of my life and a heavy object sitting on my chest and I just passed out.
"It's like a taboo, they don't tell you about it. You cannot tell anybody."
Female genital mutilation
Includes "the partial or total removal of the female external genitalia or other injury to the female genital organs for non-medical reasons"
Practised in 29 countries in Africa and some countries in Asia and the Middle East
An estimated three million girls and women worldwide are at risk each year
About 125 million victims estimated to be living with the consequences
It is commonly carried out on young girls, often between infancy and the age of 15
Often motivated by beliefs about what is considered proper sexual behaviour, to prepare a girl or woman for adulthood and marriage and to ensure "pure femininity"
Dangers include severe bleeding, problems urinating, infections, infertility and increased risk of newborn deaths in childbirth
In December 2012, the UN General Assembly approved a resolution calling for all member states to ban the practice.