Bensouda issued a statement saying war crimes, crimes against humanity and genocide -- all crimes that may be occurring in the Central African Republic -- fall under her jurisdiction.
"I hereby call upon all parties involved in the conflict, including former Seleka elements and other militia groups, such as the anti-Balaka, to stop attacking civilians and committing crimes, or risk being investigated and prosecuted by my office," she said Monday.
Seleka, formally disbanded, refers to the Muslim rebel coalition that toppled the CAR government in March. Ongoing conflict has taken a turn for the worse as Christian militias, dubbed anti-Balaka, take up arms against their Muslim rivals.
The International Committee of the Red Cross said recent fighting near Bangui has left at least 300 people dead and the number keeps rising.
"The death toll is rising, the majority of the population has no access to health facilities because of the insecurity and the bodies are still collected daily in the affected zone," the U.N. Office for the Coordination of Humanitarian Affairs said in a separate statement Monday.
The U.N. Security Council approved a resolution for French military support of an African Union peacekeeping force in CAR. France 24 reported Tuesday two French soldiers died as a result of wounds suffered during a battle in Bangui.