Sudan, which has rejected a return to the negotiating table, accused South Sudan of undermining its stability by backing rebels inside its territory despite international appeals for it to stop.
The "South Sudan government did not respond to the repeated calls of the international community and continued its hostile activities to undermine the stability and security of Sudan," said the foreign ministry.
The statement, carried by SUNA state news agency late on Monday, followed a new wave of Sudanese air raids against the South that drew swift condemnation from the United Nations, United States and France.
It came after Sudan's President Omar al-Bashir ruled out any future talks with rival South leader Salva Kiir, who was in Beijing to drum up support from China, a traditional Khartoum ally.
Sudan accuses the South of supporting anti-government rebels from its conflict-hit western region of Darfur as well as those fighting in Blue Nile and South Kordofan states.
The South, which split from Sudan in July 2011 following an independence referendum, denies backing opposition movements in the north.
UN leader Ban Ki-moon, meanwhile, deplored the cross-border air raids, and called on Bashir and Kiir to stop the "slide" to war after months of escalation along their oil-rich border.
"The secretary-general condemns the aerial bombardment on South Sudan by Sudanese armed forces and calls on the government of Sudan to cease all hostilities immediately," said deputy UN spokesman Eduardo del Buey.
Ban said "there can be no military solution to the disputes between Sudan and South Sudan.
He urged "President Bashir and President Kiir to stop the slide toward further confrontation and urges both sides to return to dialogue as a matter of urgency," the spokesman added.
US President Barack Obama, while calling on Sudan to cease its aerial bombardments, has said South Sudan "must end its support for armed groups inside Sudan and it must cease its military actions across the border."
In its statement, the Sudanese foreign ministry said rebels were behind an attack on a joint Sudanese-Chadian-Central African border force in Darfur.
Eleven Central African troops died in the rebel attack last week on the Sudanese side of the border, officials in Bangui said earlier.
The ministry also referred to repeated rebel attacks on the South Kordofan town of Talodi.
Insurgents from the Sudan People's Liberation Movement-North (SPLM-N) claimed to control part of the strategic town on Sunday night, denying they had suffered heavy losses on the same day South Sudanese forces ended their occupation of the key Heglig oilfield in the southern region.
The foreign ministry "affirmed that the armed forces maintain the legitimate right ... to practise self defence and to pursue the aggressors wherever they are," the statement on SUNA said.
South Sudan said Sunday it had completed a withdrawal of its forces from the disputed oil town of Heglig, but on Monday air raids were staged on Bentiu, the capital of the South's Unity state.
Bashir, making a visit to Heglig, said the time was over for talks with Kiir's government, which he has previously described as an "insect" that must be eliminated.
"No negotiation with those people," Bashir told soldiers in Heglig, which the South occupied for 10 days. "Our talks with them were with guns and bullets."
On Friday, Bashir and Defence Minister Abdelrahim Mohammed Hussein -- both wanted by the International Criminal Court for alleged war crimes in Darfur -- declared the army had forced Southern soldiers out of Heglig.
Kamal Marouf, a Sudanese army commander, claimed in Heglig on Monday that more than 1,000 South Sudan troops were killed in the clashes.
But Kiir had already announced that his forces would leave under "an orderly withdrawal" from Heglig, in response to appeals from world leaders and to allow a resumption of dialogue.
Unity Governor Taban Deng said Sudanese bombs nonetheless fell on a key bridge and a market, killing at least two children in Bentiu.
"We have been pressured by the international community to pull out of Heglig and this is the consequence -- we have brought the war to home," Deng said.
Sudan denied the attack but the United States condemned it and urged an "immediate" halt to hostilities and a return to talks.
Mac Paul, the South's deputy director of military intelligence, called the attack "a clear provocation."
The violence in Heglig was the worst since South Sudan won independence after a 1983-2005 civil war in which an estimated two million people died.
In Beijing, Kiir was expected to plead his case to Chinese authorities, but analysts said China was unlikely to take sides and would keep pushing for dialogue.