A member of the U.N. staff was killed and another was injured this week in attacks in Abyei, a disputed region along the border between Sudan and South Sudan.
A statement issued by a spokesman for Ban said the secretary-general was "extremely concerned" about the region.
"He urges the Abyei communities to return to calm and resolve their disputes through dialogue," a statement from the spokesman read.
South Sudan last year gained independence as part of a peace deal that ended the Sudanese civil war. Border demarcation remains one of the outstanding issues left from the 2005 peace deal.
Elsewhere in the region, Aichatou Mindaoudou, acting head of the U.N.-African Union hybrid peacekeeping mission in Sudan's restive region of Darfur expressed concern about a "pattern of conflict" in the region. Violence, she said, "is a dead end that only harms the people of Darfur."
UNAMID peacekeepers last week were blocked from investigating attacks in Darfur recently that left at least 13 people dead.