Sudanese warplanes on Tuesday carried out air raids on South Sudan, officials in that country said, threatening a rapprochement between the neighbors.
In a statement, the 15 Council members said they "demand that all parties cease military operations in the border areas and put an end to the cycle of violence."
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The statement, read by Britain's UN envoy Mark Lyall Grant, also called on the two countries "to exercise maximum restraint and sustain purposeful dialogue," and to "take no action that would undermine the security and stability of the other, including through any direct or indirect form of support to armed groups in the other's territory."
The bombing was Khartoum's response to an attack launched by the South with heavy weapons on an oil field "inside Sudanese territory," said Sudanese foreign ministry spokesman Al-Obeid Meruh.
Sudan suspended an April 3 summit between President Omar al-Bashir and his southern counterpart Salva Kiir in Juba following Monday border clashes. Southern officials however said the invitation still stood.
Council members said they were "deeply alarmed" by the border violence, "which threatens to precipitate a resumption of conflict between two countries and worsen the humanitarian situation."
They also reiterated the "grave urgency to deliver humanitarian aid ... in order to avert a worsening of the serious crisis in South Kordofan and Blue Nile."
The UN's refugee agency warned that the bombings put the lives of more than 16,000 Sudanese refugees at risk.
Sudan's UN ambassador, Daff-Alla Elhag Ali Osman, told reporters that there never was an aerial bombardment, and that the humanitarian situation in both the Blue Nile and Southern Kordofan was "very normal."
"There is not any kind of crisis," the ambassador said.
UN Secretary General Ban Ki-moon earlier called on both countries to end the clashes and respect the agreements on border security they had already reached.
Border tensions have mounted since South Sudan split from Sudan in July after an overwhelming vote for secession following a 20-year civil war that left some two million people dead.
