He said the girls, who were subjected to poverty, early marriage, female genital mutilation, abuse and other violations hold great potential for progress in the world.
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Eliasson made this known at a High-Level Forum on Adolescent Girls and the 2030 Agenda on Friday in New York, organised by the UN Population Fund (UNFPA) in collaboration with UN Women.
He added that studies had shown that the longer girls stayed in school the more they earn and the smaller the families they chose to have , the better society would be.
``Each year of secondary schooling increases girls’ future wages by up to 20 per cent.
``When women and girls earn income, they reinvest 90 per cent of it into their families; that is two or three times as much as men do.
``The UN has a mandate for gender equality since the day it was founded.''
Eliasson also said that the SDGs aimed to ensure access to sexual and reproductive health information and services ``to avoid unwanted pregnancy and stop the spread of sexually transmitted diseases.
``Under the SDGs, females are to be spared genital mutilation which causes so much lasting damage. Girls must also be protected from other harmful traditional practices and as such, the Goals call for high-quality education for girls.
``Girls should also have a voice in decisions that affect them and their lives. We should not only work for young people, we should also work with them.''
The deputy secretary-general said the UN "HeForShe" campaign brought millions of men and boys together for gender equality, noting that ``when we achieve progress for girls, we will see advances across all of society.''
He explained that the UNFPA and UNICEF launched a global programme to accelerate action to end child marriage.
Their Joint Programme on Female Genital Mutilation, he added, helped to push communities which were home to 12 million people to abandon the practice.