Sudanese warplanes launched fresh air raids on oil-rich areas of South Sudan, a Southern official said, threatening a tentative rapprochement despite international calls for calm.
Earlier, Sudan suspended an April 3 summit between President Omar al-Bashir and his southern counterpart Salva Kiir in Juba following border clashes on Monday, although Southern officials later said the invitation still stood.
"After a day of attacks by air and ground troops on Monday, this morning we heard the Antonov (aircraft) return, and dropped two bombs," said Gideon Gatpan, information minister for South Sudan's Unity state.
He believed the air strikes had targeted oilfields but there was no apparent damage.
Sudanese foreign ministry spokesman Al-Obeid Meruh said the bombing was Khartoum's response to an attack launched by the South with heavy weapons on an oilfield "inside Sudanese territory".
Kiir, however, said northern bombers and ground troops had struck first on Monday, moving into Unity State before Juba's troops fought back and took the Heglig oil hub.
The Sudanese army said calm had returned on Tuesday and northern troops were "fully in control of the Heglig area".
US Secretary of State Hillary Clinton said Khartoum bore the brunt of the blame for the "deeply distressing" border clashes.
"The weight of responsibility rests with Khartoum," Clinton told reporters in Washington, citing aerial bombing runs by the Sudanese government as "evidence of disproportionate force".
A statement from the 15-member United Nations Security Council called on both sides to end the violence, to exercise "maximum restraint" and do nothing to undermine security in the region.
Council members said they were "deeply alarmed" by the violence, and reiterated the "grave urgency to deliver humanitarian aid … in order to avert a worsening of the serious crisis in South Kordofan and Blue Nile".
United Nations chief Ban Ki-moon called on both countries to respect existing agreements on border security they had already reached, said spokesman Martin Nesirky.
South Sudan's Information Minister, Barnaba Marial Benjamin, said his country would not resume fighting despite the clashes, and left the door open for next week's summit.
"Our invitation to President Omar al-Bashir still stands as it is," Benjamin told reporters. "We are ready for any dialogue."
But Mohammed Atta, the chief of Sudan's powerful intelligence service, told reporters Tuesday night that the conditions were not right.
"The atmosphere now is not healthy for negotiation," he said after Monday night's clashes.
The latest fighting follows a controversial "framework agreement" reached earlier this month at African Union-led talks in Addis Ababa.
It gives nationals of each state the right to live, move and carry on economic activities in the other.
Magdi El Gizouli, a fellow at the Rift Valley Institute, said it was "highly plausible" that the Sudanese armed forces had launched an attack on a disputed part of the border "with the intention of spoiling this whole rapprochement between north and South Sudan."
He said an Islamist bloc in the Sudanese elite, with considerable support within the armed forces, strongly opposed the framework deal.
But there are also elements in South Sudan "who think they can bring down Khartoum," he added.
Another analyst, El Shafie Mohammed El Makki, said that without clear evidence as to who struck first the exact reason for the clash was unclear.
However, the analysts said they did not expect a return to full-scale war.
The UN's refugee agency warned that the bombings put the lives of more than 16,000 Sudanese refugees at risk and urged those who had escaped the fighting between rebels and government troops in Sudan's South Kordofan, to move on.
Both Heglig and the area bombed on Tuesday are run by the Greater Nile Petroleum Operating Company (GNPOC), a consortium led by China's state oil giant CNPC.
Although both countries claim parts of the Heglig area, Gizouli said it "is firmly in north Sudan".
Sudanese state radio reported early Tuesday that Khartoum had suspended Bashir's visit to Juba "after the South Sudanese army attacked Heglig".
The proposed talks between Bashir and Kiir had been aimed at easing tensions that pushed the two countries to the brink of war as recently as early this month.
Border tensions have mounted since South Sudan split from Sudan in July last year after an overwhelming vote for secession that followed Africa's longest war.
Earlier this month, after months of failed negotiations, a dispute over oil fees and mutual accusations of backing rebels on each other's territory, South Sudan's chief negotiator Pagan Amum said relations had improved.
Amum and a South Sudanese delegation visited Khartoum last week to invite their "brother" Bashir to the summit and said he had accepted.
