The government, hosting a one-day London summit on FGM and forced marriage, also announced 1.4 million pounds ($2.4 million) of funding for an prevention programme.
It also said it would enact legislation that would see parents prosecuted if they fail to prevent their daughter undergoing such a practice.
"It's absolutely clear what we are trying to achieve...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," Cameron said.
He urged countries to sign up to an international charter, launched at the summit, which calls for the eradication of both practices and said 21 countries had already done so.
FGM, the partial or total removal of external female genitalia, is a tradition practised widely in many African and Muslim countries and often justified as a means of suppressing a woman's sexual desire to prevent "immoral" behaviour.
Around 103,000 women aged between 15 and 49, and another 10,000 girls aged under 15 who have migrated to England and Wales are estimated to have undergone FGM, according to a report on Tuesday from City University London.
Worldwide, more than 130 million girls and women have undergone FGM and more than 700 million women alive today were children when they were married.
Ministers and officials from Pakistan, Somalia, Ethiopia, India, Bangladesh, Burkina Faso, Zambia and others also pledged to step up efforts to tackle both issues.
But UNICEF warned that population growth, particularly in Sub-Saharan Africa, meant the number of FGM victims would soar and there would be no decline in the number of child brides unless global action was dramatically accelerated.
Cameron said ending FGM and child marriage was a global challenge on a par with eradicating poverty and tackling diseases.
"We are dealing with a preventable evil. This does not need to happen," he told the summit attended by more than 500 delegates from 50 countries.