The government of north Sudan is demanding the south withdraw its troops from two key border states by Wednesday.
The demand, reported in Sudanese media, concerns the states of Blue Nile and South Kordofan.
Both sit along Sudan's north-south border, like the disputed and oil-rich Abyei region, which northern forces occupied a little more than a week ago.
The two states are currently under northern control but were battlegrounds during Sudan's long north-south civil war.
The south is due to declare independence July 9 after voting to split from the north in a January referendum.
Analysts warn the south may choose to fight for Blue Nile and South Kordofan, after saying it would not allow the Abyei dispute to drag it back into war.
On Sunday, an international monitoring group warned that northern Sudanese forces appear to be destroying Abyei's main town in a possible act of war crimes.
The Satellite Sentinel Project also said it had photos showing a buildup of tanks, trucks, artillery, and infantry fighting vehicles in Abyei. It said the forces are "all capable of rapid forward movement."