UN Secretary-General Ban Ki-moon has condemned Sudan's bombardment of a border area in South Sudan.
Mr Ban called on "the government of Sudan to cease all hostilities immediately", saying there could be no no military solution" to the two countries' simmering border dispute.
On Monday Sudanese warplanes dropped bombs near the South Sudanese town of Bentiu, witnesses said.
Later, Sudanese leader Omar al-Bashir ruled out talks with South Sudan.
Mr Bashir was speaking while visiting the oil field and border town of Heglig, which South Sudanese troops had occupied for nearly two weeks.
South Sudan says its forces withdrew from Heglig, but Sudan says it expelled them, killing 1,000 soldiers.
"We will not negotiate with the South's government, because they don't understand anything but the language of the gun and ammunition," Reuters news agency quoted Mr Bashir as telling troops on his arrival in Heglig.
The past few months have seen sporadic fighting in the oil-rich areas along the two countries' undemarcated border, prompting concern the violence could escalate into a full-blown war.
Mr Ban called on Mr Bashir and South Sudanese President Salva Kiir "to stop the slide toward further confrontation and... to return to dialogue as a matter of urgency".
US President Barack Obama has said both countries "must have the courage" to return to the negotiating table and resolve their differences peacefully.
However, Sudan's ambassador to the UN Daffa-Alla Elhag Ali Osman accused the South of "aggression" and said his country had the right to defend itself.
"We have been targeted by... the South. We have every right to militarily repel that attack and aggression," Mr Osman told the BBC's World Today programme.
"Let me make it clear: We will not cross the international border and attack the South... inside their territories," he added.
'Declaration of war'
Sudan's military commander Kamal Marouf said that 1,000 southern soldiers had been killed during the fighting for Heglig, reports the AFP news agency, whose correspondent saw an "uncountable" number of dead bodies wearing South Sudanese military uniforms.
But these casualty figures were rejected by South Sudan's Information Minister, Barnaba Marial Benjamin, who told the BBC's Focus on Africa programme that "not even a single SPLA soldier have they killed".
The air raid by Sudanese forces on the South Sudanese border town of Bentiu killed at least one person, according to witnesses.
Taban Deng, governor of Unity state, said the bombs fell on a key bridge, which leads to the border, and a market between the state capital Bentiu and the nearby town of Rubkona.
The witnesses described seeing a huge plume of smoke rising from a market and the body of a dead boy.
Mr Deng said that three civilians had also been critically wounded in the raid and were not expected to survive.
South Sudan's deputy head of intelligence, Mac Paul, described the bombing as a "declaration of war", according to the Associated Press.
The UN Security Council demanded that South Sudan withdraw its forces from Heglig and the neighbouring Abyei regions, as well as a "complete, immediate, unconditional" end to all fighting.
It also called on Sudan to stop aerial bombing raids on South Sudanese territory.
On Sunday, South Sudan's army said its withdrawal from the area was complete.
Satellite pictures of the Heglig area released on Sunday suggest key oil installations were badly damaged in the fighting and are no longer operating.
Meanwhile, South Sudan's President Kiir has arrived in China for a six-day visit during which he will meet his Chinese counterpart, Hu Jintao.
China has traditionally been an ally of diplomatically-isolated Sudan, but observers say Chinese officials are likely to push for an end to hostilities, as it is the major buyer of oil from both countries
The former rebel Sudan People's Liberation Movement (SPLM) has governed South Sudan since it seceded from Sudan after an overwhelming vote in favour of independence in a July 2011 referendum.
The vote was the outcome of the 2005 Comprehensive Peace Agreement, which put an end to the 22-year civil war between the former north and south of Sudan. About 1.5 million people are though to have lost their lives in the conflict.
The new state took most of the former united Sudan's oil reserves with it, but relies on pipelines to seaports in Sudan to export it.
In January, South Sudan decided to shut down oil production, which provides 98% of the government's revenue, after Khartoum impounded South Sudanese oil shipments amid a dispute over transit fees.