The report, which says more than 125 million girls and women have been subjected to the ordeal, shows that many men and women want to stop FGM but they feel obliged to continue the tradition because of social pressure.
FGM, which is predominantly found across a swathe of Africa and the Middle East, involves the partial or total removal of the external genitalia. In its most extreme form, the vaginal opening is sewn closed.
Although many countries have banned the practice, it remains deeply entrenched. Campaigners against FGM say girls who are not cut are often ostracised. Many families from both Muslim and Christian communities also believe FGM is a religious requirement even though it is not mentioned in the Koran or Bible.
"(FGM) is a violation of a girl's rights to health, well-being and self-determination," UNICEF Deputy Executive Director Geeta Rao Gupta said as the report was launched. "What is clear from this report is that legislation alone is not enough. The challenge now is to let girls and women, boys and men speak out loudly and clearly and announce they want this harmful practice abandoned."
FGM, which is thousands of years old, is often seen as a manifestation of patriarchal control, but the report shows a growing number of men and boys oppose the ritual. One of several surprise findings is that in three countries - Chad, Guinea and Sierra Leone - more men than women want FGM to end.
UNICEF says girls and women consistently underestimate the proportion of boys and men who are against FGM and that the tradition is being kept alive partly because of a lack of communication on the issue, which is often shrouded in secrecy.
Data shows the practice is declining in more than half the 29 African and Middle Eastern countries studied in the report and has fallen quite dramatically in some.
In Kenya, girls between 15 and 19 are three times less likely to have been cut than women 30 years older. Prevalence has also halved among adolescent girls in Benin, the Central African Republic, Iraq, Liberia and Nigeria.
But there has been no significant change in Chad, Djibouti, Gambia, Guinea Bissau, Mali, Senegal, Somalia, Sudan and Yemen. The lack of any marked decline in Senegal is particularly surprising given that campaigners often hold it up as a shining example of a country making a truly concerted effort to eliminate the practice.
In most countries the main justifications cited for FGM are social acceptance and preservation of virginity.
FGM, which is often carried out with unsterilized instruments, can cause severe health and psychological problems. In some cases, girls bleed to death or die from infections. Later in life, FGM can lead to complications in childbirth and increase the risk of the mother and/or baby dying.
The report says there has been a move towards less severe types of cutting in some countries. In Djibouti, 83 percent of women aged 45-49 reported being sewn up compared to 42 percent of girls aged 15-19. But UNICEF says governments, aid agencies and others should be promoting an end to FGM rather than encouraging milder forms.
Another trend in some countries is towards medicalising the procedure - something that has alarmed campaigners. Traditional cutters usually perform FGM but in Egypt, Kenya and Sudan doctors and other health workers also carry it out.
The report recommends encouraging greater public scrutiny of FGM within social groups in order to challenge the misconception that everyone else in that community approves of the practice.
Finding ways to expose hidden opposition to FGM will empower parents who do not want to cut their girls and help build a critical mass against the practice. Collective declarations against FGM - as have happened in communities in Ethiopia, Gambia and Senegal- are effective ways to highlight the erosion in social support for the practice, the report adds.
UNICEF also emphasises the need to engage boys and men in ending FGM and underlines the importance of girls' education in bringing about change. Data shows that higher levels of education among mothers corresponds to a lower risk of their daughters being cut. UNICEF says the three-year-study, which draws on data from 74 surveys, will help governments, international agencies and grassroots organisations fine-tune programmes aimed at eradicating FGM.
By Guylain Gustave Moke