Sudan exports billions of dollars of oil per year. Southern states produce more than 80% of it, but receive only 50% of the revenue, exacerbating tensions with the north. The oil-rich border region of Abyei is to hold a separate vote on whether to join the north or the south.
The Sudanese town of Abyei has been set on fire, with gunmen looting property, the UN says.
The town and surrounding area are claimed by both Khartoum and by South Sudan, set to become independent in July. The town was captured at the weekend by northern troops.
The UN has urged Sudan's government in Khartoum to withdraw its forces.
South Sudan's secession follows decades of north-south conflict and some fear this dispute could reignite the war.
'Act of war'
In a statement, the UN Mission in Sudan (Unmis) said it "strongly condemns the burning and looting currently being perpetrated by armed elements in Abyei town".
It stressed that the northern troops were "responsible for maintaining law and order in the areas they control", urging Khartoum to "intervene to stop these criminal acts".
South Sudan earlier denounced the Abyei takeover on Saturday as an act of war.
A southern military spokesman told the BBC the north had attacked the area with 5,000 troops, killing civilians and southern soldiers.
Some 20,000 people, almost the whole population of the town, had fled, aid agency Medecins Sans Frontieres (MSF) told the BBC.
Khartoum has said it acted after 22 of its men were killed in a southern ambush last Thursday. The northern troops were travelling in a UN convoy.
UN officials have described the incident as "a criminal attack" and the US called on South Sudan to "account" for the assault.
South Sudanese forces have denied responsibility for the incident.
Since then, both UN Secretary General Ban Ki-moon and EU top diplomat Catherine Ashton have condemned the violence in the region.
On Sunday, UN Security Council envoys said during a visit to Khartoum that the north should "withdraw immediately" its troops from the Abyei region. The diplomats have now arrived in South Sudan.
Tension over Abyei - a small town claimed by a southern group, the Dinka Ngok, and northern nomads, the Misseriya - has been rising since a referendum on its future scheduled for January was postponed.
Since then there have been fears clashes in the region could spark a new war between the northern-based government of Sudan and the soon-to-be independent South Sudan.
Under a 2005 peace agreement, which ended 22 years of civil war, Abyei was granted special status and a joint north-south administration set up in 2008.