The President of South Sudan, Salva Kiir, has said he will not withdraw his troops from the Heglig oilfield on its disputed border with Sudan.
Speaking in parliament, Mr Kiir defied calls from the UN and African Union to pull out troops, after days of clashes with Khartoum.
Meanwhile, Sudanese aircraft are reported to have attacked Unity state in the South.
The fighting is the worst since South Sudan gained independence last July.
Speaking in Geneva, UN Secretary General Ban Ki-moon said he was gravely concerned about the situation and urged both governments to "cease hostilities immediately" and hold a presidential summit to negotiate a solution.
He said: "War would only compound the already considerable sufferings of the people of Sudan and South Sudan.
"What is required is a political will and political leadership at the moment of need. This crisis requires the full and urgent attention of the international community."
On Wednesday, Sudan admitted that South Sudan had seized the town of Heglig, which is home to facilities that account for around half of Sudan's oil production.
The area is internationally recognised as Sudanese territory, but South Sudan disputes this.
South Sudan says it took Heglig in order to prevent the Sudanese army organising attacks from there.
In response, Sudan ordered a general military mobilisation and has vowed to act with "all means" against the attack. It has also pulled out of African Union-led negotiations with South Sudan.
'Meaningless war'
In parliament on Thursday, Mr Kiir said he did not want war with Khartoum, but said his country had to act in self-defence.
"I always say we will not take the people of South Sudan back to war, but if we are being aggressed (attacked) like this we will have to defend ourselves," he said.
"I am appealing to the citizens of the Republic of Sudan, especially the mothers, not to allow their children to be dragged into a meaningless war," he added.
Meanwhile, Sudanese aircraft dropped five bombs on a bridge linking Bentiu and neighbouring Rubkotna, in Unity state, leaving at least one dead and three injured, according to South Sudan officials.
On Wednesday, the African Union said it was deeply alarmed by the clashes, and called on both sides to exercise the utmost restraint.
In a statement, the AU called upon both countries to resolve this and all other outstanding issues "in a peaceful way in accordance with the overriding principle of establishing two viable states in Sudan and South Sudan".
Correspondents say Sudan, having lost most of its oil when the south seceded, will not tolerate losing any more.
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