South Sudanese President Salva Kiir on Friday ordered the immediate withdrawal of his troops from the contested Heglig oil field, seized from Khartoum's army on April 10, sparking fears of wider war.
"The Republic of South Sudan announces that the SPLA (Southern army) troops have been ordered to withdraw from Panthou-Heglig," Information Minister Barnaba Marial Benjamin said, reading out a presidential statement.
In a related development, Rebels in the eastern border state of Blue Nile claimed dozens of government dead on Friday as unrest spread within Sudan, 10 days after a deadly standoff with the South erupted over a major oilfield.
In Sudan's western Darfur region, peacekeepers expressed concern that rebels were exploiting the Sudan-South Sudan border fighting, which is the most serious since the South's independence last year and has sparked fears of all-out war.
Further ramping up diplomatic pressure to restrain the two nations, United Nations chief Ban Ki-moon condemned South Sudan's seizure of Sudan's main oilfield, Heglig, as "illegal".
Ban urged South Sudan to withdraw its forces immediately.
"This is an infringement on the sovereignty of Sudan and a clearly illegal act," he told reporters.
The UN secretary general said Sudan, for its part, had to "immediately stop shelling and bombing South Sudanese territory and withdraw its forces from disputed territories, in particular Abyei".
"Both must stop supporting proxy forces against each other," he added.
While there was no immediate confirmation of fresh fighting between Sudan and the South on Friday, rebels in Sudan's Blue Nile said they had killed 79 government troops and militiamen in two ambushes in the ethnically divided state.
The attacks came on Tuesday and Wednesday in mountainous terrain about 35 kilometres (20 miles) south of the state capital Ed Damazin, said Arnu Ngutulu Lodi, spokesman for the rebel Sudan People's Liberation Movement-North (SPLM-N).
The group, which was a civil war ally of the former rebels who now rule South Sudan, has been fighting for several months in Blue Nile and South Kordofan states, both of which border the South.
Lodi, whose forces deny being supported by the South, said there has been an upsurge in fighting in Blue Nile since border clashes between Sudan and South Sudan escalated last week with waves of air strikes hitting the South, and Juba seizing the north's Heglig oil hub on April 10.
Heglig is part of South Kordofan.
Lodi alleged Khartoum is using the Heglig standoff as an opportunity to mobilise militias and other fighters against the SPLM-N. "That's how we see it," he said.
In Darfur, where unrest continues almost a decade after rebels drawn from non-Arab ethnic groups rose up against the Arab-dominated Khartoum government, peacekeepers expressed concern after three separate rebel attacks last Tuesday.
"In the climate of ongoing tensions between Sudan and South Sudan, I am deeply concerned that armed movements are seeking to destabilise Darfur," said Ibrahim Gambari, head of the United Nations-African Union peacekeeping mission (UNAMID).
He said such actions could undermine progress towards peace made since the government last year signed a deal in Qatar with an alliance of Darfur rebel splinter factions.
The Sudan Liberation Army (SLA)-Minni Minnawi faction claimed the most serious attack, on a Sudanese Armed Forces compound.
"In this fighting we used heavy weapons and bombed the area from far away," the group's spokesman Abdullah Moursal told AFP. "This area is now under the control of the SLA."
Sudan's army spokesman could not immediately be reached.
The UN's Ban said countries with influence on the governments of Sudan and South Sudan "must step up their efforts at this critical moment."
After talks in Khartoum and in the South's capital Juba, Princeton Lyman, US special envoy on Sudan and South Sudan, said that the two sides wanted a way out.
He said he was pressing the South to withdraw from the Heglig oil field.
"I can say with confidence that virtually everyone I've talked to has said, look, we don't want to go to all-out war with the other," Lyman told reporters.
Lyman acknowledged the neighbours were in a "very, very serious crisis" but said both sides were mindful of international pressure.
Although South Sudan disputes it, Heglig has been internationally regarded as part of Sudan.
Sudan's President Omar al-Bashir has kept up war rhetoric that sparked concern from Washington.
On Thursday, the beret-wearing Bashir told a rally of freshly-trained paramilitary troops, some riding camels, that Sudan will teach the Southern government "a lesson by force."
A day earlier, he called the Juba regime an "insect" that Sudan aims to eliminate.
The South separated following a referendum organised under a peace deal that ended Sudan's 1983-2005 civil war in which about two million people died.