Sudan's armed forces are on the outskirts of Heglig town and are advancing toward the settlement, which was occupied by South Sudan this week, a Sudanese military spokesman said.
"We are now on the outskirts of Heglig town," Al-Sawarmi Khalid Saad told reporters in Khartoum. "The armed forces are advancing toward Heglig town ... the situation in Heglig will be resolved within hours."
He added that South Sudan had tried but failed to control "all of South Kordofan state".
Al Jazeera's Nazanine Moshiri, reporting from Juba, the capital of South Sudan, said that the army from Khartoum is advancing on Heglig town. "The South Sudanese military spokesperson told us that the Sudanese are around 30 km from Heglig, and if they do try and take it the South Sudanese have said they will defend themselves."
"This could end up becoming a full-blown conflict."
World powers have urged restraint after the latest round of heavy fighting that broke out on Tuesday with waves of aerial bombardment hitting the South, whose troops seized the Heglig oil region from Khartoum's army.
South Sudan seized the Heglig oilfield near the border on Tuesday. The African Union denounced the occupation as illegal and urged the two sides to avert a "disastrous" war.
Heglig, which the south claims as its own, is vital to Sudan's economy because it has a field accounting for about half of its 115,000 barrel-a-day oil output. The fighting has stopped crude production there, officials say.
South Sudanese armed forces spokesman Philip Aguer said he had not received reports of fighting in Heglig on Friday, but that the situation there should become clearer on Saturday.
"If they are advancing, the SPLA is ready to defend itself and its territories," he said by phone. "When they (Sudan's army) were pushed out of the area, they were occupying it by force, so if they want to come back by force, they can try it."
Speaking in Nairobi, Pagan Amum, South Sudan's lead negotiator at talks to resolve the dispute with Sudan, said his country was ready to withdraw under a UN-mediated plan.
"On the ground, we are ready to withdraw from Heglig as a contested area ... provided that the United Nations deploy a UN force in these contested areas and the UN also establish a monitoring mechanism to monitor the implementation of the cessation of hostilities agreement," he told reporters.
Amum said there were seven disputed areas and called for international arbitration to end the dispute over these regions.
Blow to the economy
The loss of Heglig's oil output is another blow to Sudan's economy, which was already struggling with rising food prices and a currency depreciating on the black market.
Amum said the Heglig facilities were "largely" damaged by fighting, but did not give details.
"Resumption of oil in that area will only come when the UN deploy their forces between the two countries and in the disputed areas and when the two countries reach agreement to resume oil production," he said.
Landlocked South Sudan shut down its own 350,000 barrel-per-day oil output in January in a row over how much it should pay to export crude via pipelines and facilities in Sudan.
Oil accounted for about 98 per cent of the new nation's state revenues and officials have been scrambling for ways to make up for the loss.
In Juba, about 200 people demonstrated at a government-organised protest against Sudan and in support of the occupation of Heglig, holding banners which read: "The people want the army to be in Heglig" and "They bomb children and women".
The UN Security Council on Thursday added its voice to the chorus of demands that Sudan and South Sudan stop the clashes.
Sudan's UN ambassador said South Sudan must heed the call or Khartoum would "hit deep inside the south".
The African Union, which had been helping mediate talks between the two countries over oil payments and other disputed
issues before Khartoum pulled out on Wednesday, also condemned the south's occupation of Heglig.
"The Council is dismayed by the illegal and unacceptable occupation by the South Sudanese armed forces of Heglig, which lies north of the agreed border line of 1st January, 1956," African Union Peace and Security Council Commissioner Ramtane Lamamra told reporters after a meeting late on Thursday.
The south seceded from Khartoum's rule last year but the two sides have not agreed on issues including the position of the border, the division of the national debt and the status of citizens in each other's territory.
Some two million people died in Sudan's civil war, fought for decades over ideology, religion, ethnicity and oil.