From July to September, there were 12 new cases reported in six peacekeeping missions in the Central African Republic, the Democratic Republic of Congo, Haiti, Liberia, Mali and South Sudan.
The UN refugee agency UNHCR reported 15 allegations, while three new cases involved staff at the International Organisation on Migration and one allegation was directed against the UN children's agency UNICEF.
One allegation at UNHCR has been substantiated, while two others are still under investigation. The other cases are being reviewed, according to UN information.
UN Secretary-General Antonio Guterres has made fighting sexual abuse by peacekeepers and UN staff a priority of his tenure.
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The UN chief is "obviously disappointed and saddened that these actions continue," said UN spokesman Stephane Dujarric.
The United Nations has been damaged by a wave of rape cases involving peacekeepers in the Central African Republic, prompting former UN chief Ban Ki-moon to fire the mission commander.
Of the 31 cases, 12 took place this year, two were from last year and six in 2015. The dates have not been established for the remaining 11 allegations.
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