Northern Sudan's army clashed with southern forces in the region this week, killing at least 14, the United Nations said Friday.
United Nations Secretary-General Ban Ki-moon said he "is deeply concerned by the continued tension" in the area.
"The military standoff is unacceptable," Ban said in a statement.
South Sudan in January voted to split from the north, and is expected to officially become an independent nation in July.
However, the fate of the oil-rich Abyei region remains a flashpoint.
Sudanese President Omar al-Bashir said last month that his government would not recognize the new state of South Sudan if it claims Abyei.
"Abyei is a part of the north and will remain a part of the north," the president said in a speech broadcast on state television.
Al-Bashir's declaration reneged on an earlier promise to honor the results. (read more)