South Sudan set conditions to pull out troops from the contested Heglig oil field seized from Khartoum's army this week, including a withdrawal by Sudan from Abyei, another disputed area.
"South Sudan would withdraw from Heglig if a guarantee can be provided that it will not be used for another attack against our territory," Information Minister Barnaba Marial Benjamin said.
"Firstly, all ground and air assaults by Sudan must end immediately," Benjamin said, three days after Southern troops wrested control of Heglig, amidst heavy clashes between the rival armies.
"The Sudan Armed Forces still occupying Abyei must also withdraw entirely," he added, referring to a contested area seized by Khartoum's forces last year.
Once that pullout is complete, "international monitors" would then have to ensure a demilitarised zone either side of the contested border until the frontier "can be demarcated under international arbitration."
South Sudan's president had said earlier in the day his nation will not withdraw its troops that this week entered a disputed border region with Sudan.
Salva Kiir, president of South Sudan, spoke to parliament on Thursday in the midst of escalating clashes along the border with Sudan and the bombing of a bridge outside Beintu in which one soldier was killed and two others injured.
"[The UN Secretary General] gave me an order," Kir said. "He said I order you to immediately withdraw from Heglig. I said I'm not under your command."
Al Jazeera's Nazanine Moshiri, reporting from Juba, the South Sudanese capital, said that South Sudan wants an international mechanism in place before they withdraw from Heglig.
"The president of South Sudan is not going to budge on this," she said. "If bombardment continues, the South Sudanese will go into the tow on Abyei, and this is of extreme concern to the international community."
On Wednesday, troops from South Sudan captured the oil-rich border town of Heglig that is claimed by Sudan, whose troops withdrew under the onslaught.
Kiir said that South Sudan's military forces, the SPLA, had also advanced past Heglig after occupying it.
"They pursued them up to the so-called Heglig. But these forces did not stop in Heglig, there was not fighting in Heglig," he said.
Sudanese warplanes attacked a major South Sudanese town at dawn, bombing the capital of the oil-producing Unity border state, according to South Sudan officials.
The aircraft targeted a strategic bridge on the Rubkhona airstrip just outside Beintu town close to a UN compound, which lies about 60km from the frontier as clashes between the recently separated nations continued for a third day.
One soldier was killed and two others injured in the attack.
'Choosing the path of war'
Sudanese President Omar al-Bashir accused South Sudan of "choosing the path of war," following days of intensifying clashes on their shared border.
"Our brothers in South Sudan have chosen the path of war, implementing plans dictated by foreign parties who supported them during the civil war," Bashir told reporters, referring to decades of conflict before the South's independence last year.
"War is not in the interest of either South Sudan or Sudan but, unfortunately, our brothers in the South are thinking neither of the interests of Sudan or of South Sudan."
Al Jazeera's Harriet Martin, reporting from Khartoum, said that under international law, Heglig belongs to Sudan, not South Sudan.
"Interestingly, in the negotiations which have been taking place Addis Ababa, there are five disputed areas under discussion but Heglig is not one of them," she said.
"The occupation of Heglig is taking [the Sudan-South Sudan] battle to a different level," our correspondent said. "What you have now is the possibility of it severely affecting the supply of oil to Sudan."
The military advances by South Sudan and the Sudanese air raids brought condemnation from the UN Security Council as UN Secretary-General Ban Ki-moon called on both sides to withdraw from the other side's territory and said he was "alarmed by the escalation in fighting".
Daffa-Alla Elhag Ali Osman, Sudan's ambassador to the UN, said he had filed a complaint to the Security Council condemning the "heinous attack" on Heglig.
"We will decide to retaliate, and retaliate severely, deep inside South Sudan if the Security Council doesn't address the situation", Ali Osman told reporters.
A statement on Khartoum's official SUNA news agency warned of "destruction" in South Sudan.
Focal point of fighting
Heglig lies along the disputed border between the two African nations and has been the focal point of nearly two weeks of clashes between their armies, which have prompted the collapse of African Union-mediated talks.
The region is home to oil fields that account for about half of Sudan's oil production, a critical source of income for the country's flagging economy.
The two rivals fought a civil war that lasted decades, and never reached a deal to share the region's oil resources or delineate their exact border during negotiations which led to South Sudan's cessation last year.
A 2009 ruling by the Permanent Court of Arbitration in the Hague placed Heglig in Sudan's Southern Kordofan region. But South Sudan has disputed the ruling, asserting that the region is in South Sudan's Unity State.
South Sudan's army said it moved into Heglig on Tuesday after repelling an attack launched by Sudanese Armed Forces against a position near the border town of Teshwin.
Bashir was scheduled to visit South Sudan for a summit April 3, but the talks were scrapped in the wake of the clashes.
Barack Obama, the US president, earlier this month called Kiir to ensure that South Sudan's military exercised maximum restraint and was not involved in, or supporting, fighting along the border.
In a statement, the African Union called upon both countries to resolve all outstanding issues "in a peaceful way in accordance with the overriding principle of establishing two viable states in Sudan and South Sudan".