The United States says Sudan and South Sudan want to find a way to avoid full-scale war as fighting continues along the two countries' border.

Following talks with officials of both governments, U.S. Special Envoy for Sudan Princeton Lyman told reporters Thursday that the two sides realize how costly war would be.

“In the discussions I have had in both Khartoum and Juba, I can say with confidence that virtually everyone I have talked to has said, 'Look, we don't want to go to all-out war with the other. We need to find a way out.'”

Lyman said South Sudan wants assurances before withdrawing from Heglig that there will be no more attacks by Sudanese-backed militias or bombing raids, as well as the withdrawal of northern troops from the town of Abyei.

Lyman says Khartoum agrees in principle to the plan, despite emotions running very high on each side and serious disagreements about what is needed to end the conflict.

Thursday, United Nations Secretary-General Ban Ki-moon said South Sudan's seizure last week of the Heglig oil fields violates the sovereignty of neighboring Sudan. He asked South Sudan to remove its forces from the oil-rich border area, which is claimed by both countries.

“I call on South Sudan to immediately withdraw its forces from Heglig. This is an infringement on the sovereignty of Sudan and a clearly illegal act.”

Mr. Ban also called on Sudan to stop shelling and bombing South Sudanese territory and withdraw from the disputed Abyei region.

In South Sudan Thursday, the country's chief negotiator, Pagan Amum, said Juba is ready to halt the fighting.

“The government of South Sudan is ready to sign the cessation of hostilities agreement that was presented to the parties by the panel on 4th of April, and we are ready to sign it now.”

Amum went on to say South Sudan wants to ensure both sides withdraw from all contested areas and settle their land disputes through international arbitration.

Sudan's president, Omar al-Bashir, is threatening full-scale war against South Sudan. Thursday, he said Sudan will teach the south's government “a lesson by force,” and vowed to retake Heglig.

The two Sudans have been unable to resolve disputes over borders, oil, and citizenship issues stemming from the south's independence last July.

African Union mediators have tried to help the sides settle their issues, but made little progress.

Starting in the 1980s, north and south Sudan fought a 21-year civil war that eventually led to southern autonomy and independence.