The warning follows South Sudan's capture of the disputed Heglig oilfield on Tuesday after a series of border skirmishes with its northern neighbor.
The escalating violence has brought the two sides closer to a full-blown conflict than at any time since the South seceded last July under a peace deal ending decades of war between the bitter enemies.
African Union Peace and Security Council Commissioner Ramtane Lamamra said the body was demanding an immediate and unconditional withdrawal of South Sudan's forces from the area, Reuters reported.
The Council is dismayed by the illegal and unacceptable occupation by the South Sudanese armed forces of Heglig, which lies north of the agreed border line of 1st of January, 1956, he told reporters following a meeting late on Thursday.
The feeling within the Peace and Security Council is that it is time now for the two leaders ... to display the required leadership so that the two countries would avoid a disastrous war which the two people do not need.
According to spokesman for SPLA, the South Sudanese army, the latest series of attacks came after South Sudanese troops were attacked by Sudanese forces on Monday in the town of Teshwin.
After repulsing the attack, SPLA troops then pursued Sudanese troops across the border into Heglig.
The Heglig oil fields are a vital strategic resource, accounting for over half of Sudan's domestic oil production.
Since South Sudan's secession, both countries have been locked in a battle for control of the ill-defined border areas.
The south has been particularly hard hit by the ongoing conflict, after it was forced to shut down its roughly 350,000 barrel-per-day oil output in January because of a dispute over how much it should pay to export crude via facilities in Sudan.
The shutdown has crippled the South Sudanese government, which relies on oil export for 98 percent of its revenue.