Thirteen of the 15 council members voted for the resolution. Russia and China abstained, arguing that the Darfur conflict is largely over.
Authorities declared a state of emergency and imposed a nighttime curfew in Beleil to help stop the clashes.
Last week's fighting between Misseriya and Rezeigat tribesmen in the restive region left at least 48 dead, a local refugee official says, and UN reports thousands of displacements after large-scale violence.
Karim Khan is in Sudan a year after he visited the country for talks on outstanding arrest warrants over crimes committed during the 2003 Darfur war under ousted president Omar al Bashir.
The UN says it estimates around 50,000 people have been displaced by the latest fighting which has spilt over into neighbouring districts of West Darfur.
UN High Commissioner for Human Rights Michelle Bachelet demands "impartial and independent" investigations into the attacks in the volatile African region.
Clashes break out in El Geneina, capital of West Darfur, residents and aid groups say, as fighting that killed scores of people in a nearby town over the weekend spreads.
Clashes in western Darfur town of Kreinik leave 168 people dead and nearly 100 wounded, a refugee aid group says, blaming Janjaweed militias for the attack.
Ali Muhammad Ali Abd-Al-Rahman faces 31 counts of war crimes and crimes against humanity for his role in a conflict almost 20 years ago.
Security officers fired barrages of tear gas canisters on protesters demanding a restoration of the transition to civilian rule, witnesses say.
Some 1,900 tonnes of food products were stored in the World Food Programme facility in the troubled western region, which has seen a spike in conflict since October.
The violence poses a significant challenge to Sudan's transitional government, which is seeking to end decades-long rebellions in Darfur and elsewhere in the African country.
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