But observers don't expect a swift breakthrough to avert all-out war.
Both sides are facing ruin because of the fighting that has flared for months along their poorly defined border and totally shut down oil production.
The clashes began after the southern government in January cut off its entire oil output of 350,000 barrels per day through a 994-mile pipeline that runs northward to the Red Sea terminal at Port Sudan.
The southern government in its ramshackle capital, Juba, claimed the Sudanese government in Khartoum had seized southern oil worth $800 million. Khartoum said Juba hadn't paid transit fees.
Without oil revenues, neither side can afford a full-scale war.
"Both economies are in a race against time, as the halt in oil production and transit fees bring their oil-dependent economies to the brink of collapse," the Financial Times reported.
The halt in oil exports from the Sudans, largely from the impoverished south that's still struggling to rebuild after two ruinous decades of war with the north, doesn't constitute a major glitch in global energy supply terms. But the simmering conflict, reigniting the 1983-2005 civil war in which 2 million people died, would destabilize East Africa and the Horn of Africa.
This region is on the cusp of a major oil and gas boom that has the potential to transform what has largely been an economically depressed zone.
Sudanese Finance Minister Ali Mahmoud says the dispute has left a $2.4 billion hole in Khartoum's state finances. Exports have slumped 83 percent. Annual inflation hit nearly 29 percent in April.
The shutdown has essentially cut off the south's oil revenues, 98 percent of state income. Oil constitutes just more than 40 percent of the north's revenues.
Some 85 percent of the oil lies in the south, mainly in border states where the heavy clashes have taken place in the last few weeks. But the landlocked south can only export through the Chinese-built pipeline running through the north.
Kornelio Koriom Mayik, governor of South Sudan's central bank, says the south's in bad shape, too.
"We're importing everything and we're drawing on reserves, so of course we have some difficulties," he said a few days ago.
"By my calculations, unless there are shocks, we can go on for another seven months without oil," using foreign reserves "in the region of $1.5 billion."
Both sides appear to have dug in their heels at talks brokered by the African Union, with no indication either is prepared to make concessions.
The most likely prospect of heading off a new war between the Arab, Muslim north and the infant state of South Sudan, which is mainly Christian and animist, appears to be intervention by China.
Beijing is the main buyer of Sudan's oil and has multibillion-dollar investments on both sides. It thus has a vested strategic interest in bringing the two sides together and has been at the center of diplomatic efforts to get them back to negotiations.
The south seeks to build a pipeline running southeast from its oilfields to Kenya's Indian Ocean ports via Uganda, cutting out the north altogether.
But, Britain's Guardian newspaper observed May 17, "South Sudan's pipe dream risks remaining just that.
"There are 1,000 factors which could set back such a project – bandits, weather, political scrapping over cost, and so on.
"The port of Lamu in Kenya, the planned sea connection for the pipeline hasn't even been built yet."
Khartoum is bitterly opposed to such a project.
South Sudanese President Salva Kiir, a former rebel commander during the civil war, visited Beijing in April seeking Chinese aid to build the pipeline. But Prime Minister Hu Jintao has refused to put up funds for the project for fear of jeopardizing China's investments in the north.
However, Beijing has hedged its bets by offering the south bank loans and emergency aid.
That's not likely to save South Sudan unless it cuts a deal with Khartoum, or its friends in Africa can drum up $7 billion, to cover lost oil income and enable it to defy the north.