About 15 million girls worldwide become child brides each year and globally, more than 700 million women were married before the age of 18.
Unless action is taken, some 1.2 billion girls will be married by 2050, says the Girls Not Brides coalition of non-governmental organisations.
Niger, Bangladesh and India have high rates of child marriages, but Zara Rapoport from the child rights group Plan said forced marriages are also prevalent in immigrant communities in developed countries.
The resolution presented by Canada and Zambia urges all states to enact laws to prevent and end forced marriages for girls, and links child marriages to development and poverty.
But Britain took the floor at the General Assembly's rights committee to express disappointment on behalf of some 20 countries over the failure of the resolution to address girls' education about their sexuality.
"Comprehensive sexuality education is essential for all adolescents and especially girls to make positive, responsible and informed decisions about their sexuality," said the British representative.
"The lack of respect for the sexual and reproductive rights of girls is at the core of this issue and we fail to do justice to the girls suffering from (child marriage) if we cannot recognise this," he said.
The Vatican representative responded that ending child marriages was linked to issues of poverty, security and traditional customs and asserted his opposition to references on reproductive rights.
The measure was adopted by consensus in the General Assembly committee and is now set to go to the full Assembly next month.