The fact-finding mission, included in a draft resolution, would also seek to identify the perpetrators of violations allegedly committed by the Rapid Support Forces and their allies in el-Fashir.
In an opening address to delegates, the UN human rights chief urged the international community to act, Reuters reported.
"There has been too much pretense and performance, and too little action. It must stand up against these atrocities – a display of naked cruelty used to subjugate and control an entire population," UN High Commissioner for human rights Volker Turk said.
Turk also called for action against individuals and companies "fueling and profiting" from the war in Sudan, and gave a stark warning about surging violence in the Sudanese region of Kordofan, with bombardments, blockades and people forced from their homes.
The fall of el-Fashir to the RSF on October 26 cemented its control of the Darfur region in the more than 2-1/2-year civil war that it has been fighting with the Sudanese army.
The draft text up for consideration by the council, seen by Reuters, strongly condemns the reported ethnically-motivated killing and use of rape as a weapon of war by the RSF and allied forces in el-Fashir.
The draft resolution stops short of mandating an investigation into the role of external actors who may be supporting the RSF, which some rights groups had called for.
The resolution also calls for the RSF and the Sudanese Armed Forces to allow life-saving aid to reach the many people who may still be trapped inside the famine-struck city.
Women fleeing the city have reported killings and systematic rape while others have described civilians being shot in the streets and attacked in drone strikes.