Amnesty International last week accused peacekeepers of the rape, and of the indiscriminate killing of a 16-year-old boy and his father, in separate incidents Aug. 2 and Aug. 3.
Secretary-General Ban Ki-moon then fired the head of the peacekeeping mission in Central African Republic, an unprecedented action.
A spokeswoman for Ban, Vannina Maestracci, said investigations by U.N. Human rights and child protection officials and U.N. Police are continuing, and information has been handed to the U.N.'s internal watchdog. Preliminary findings will not be published to protect the confidentiality of victims and witnesses, she said.
U.N. Peacekeepers have been in the country since September 2014 to try to calm deadly violence between Christians and Muslims, which has forced thousands of Muslims to flee the country.
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Amnesty International said last week that the girl was reportedly raped by a U.N. Police officer, meaning that U.N. police are investigating one of their own members.
"Our hope is that the process of healing for this young girl can now begin," Lake said.
Maestracci said the U.N. "is determined to ensure that acts of misconduct, including sexual violence by its personnel, should not go unpunished."
The United Nations, however, has no powers of criminal investigation or prosecution, leaving that up to peacekeepers' home countries.
Since its creation in April 2014, Ban said the peacekeeping mission in Central African Republic has received 57 cases of misconduct, including 11 allegations of sexual exploitation and abuse. The mission is also being investigated over how it handled several child sexual abuse allegations against French troops last year.