South Sudan on Sunday accused Sudan of launching fresh air strikes against the new nation, but Khartoum denied that, saying it had repulsed a major rebel attack on a town in its South Kordofan state.
The war of words came after weeks of border fighting between the two neighbours that have brought the former civil war foes closer to a full-blown war.
Mac Paul, deputy director of South Sudan's military intelligence, said Sudan had launched air strikes after Southern troops left the disputed oil field of Heglig.
Sudan had attacked positions manned by South Sudan's army or SPLA in Teshwin on the southern side of the border with ground forces and war planes, he added.
Later on we had so many waves of attacks by SAF (Sudanese armed forces) deep inside South Sudan, he told reporters in the oil border town of Bentiu.
It is a provocation because there have been both ground and aerial attacks in Teshwin (and aerial attacks in) Panakuach and Unity today and as I talk the Antonov is still hovering, he said.
Four SPLA soldiers had been killed and eleven wounded, he added, while an unknown number of Sudanese soldiers had been killed.
However, Sudanese army spokesman al-Sawarmi Khalid denied the air force had launched any air strikes on Sunday.
Instead, he said that the Sudanese army had repulsed a major rebel attack on the strategic town of Talodi in its South Kordofan state, on its own side of the border.
Dozens of the rebels were killed. The army is expelling the remaining rebel forces, he added.
There was no immediate comment from the Sudan People's Liberation Movement-North (SPLM-N), a rebel group who have been fighting the Sudanese army in the South Kordofan and Blue Nile states since last year.
Khartoum accuses the South of backing the border state rebels, an allegation Juba denies.
Tensions between the two countries have been rising since South Sudan split from Sudan and became an independent country in July, taking with it most of the country's known oil reserves, the lifeline of both economies.
South Sudan's army said on Sunday it had completed a withdrawal from the disputed oil field of Heglig it had seized earlier this month, bowing to demands from the U.N. Security Council.
On Sunday, South Sudanese officials showed reporters an oil field in Unity border state which they said had been bombed by the Sudanese air force last week.
A Reuters reporter saw three bomb craters at an oil field run by the Greater Nile Petroleum Operating Co (GNPOC) but no visible damage to facilities.
The countries are at loggerheads over the demarcation of their shared border and other disputes have halted nearly all the oil production that underpins both economies.
South Sudan won its independence in a referendum that was promised in a 2005 peace accord that ended decades of civil war between Khartoum and the south. Religion, ethnicity and oil fuelled that conflict, which killed about 2 million people.
Recent tensions between Sudan and South Sudan have been fuelled by a dispute over how much the landlocked South should pay to export oil via Sudan.
Juba shut down its roughly 350,000 barrel-a-day output in January, accusing Sudan of seizing some of its crude. Oil accounted for about 98 percent of the South's state revenues.
Limited access to the remote border conflict areas makes it difficult to verify the often contradictory statements from both sides.
(Reporting by Ulf Laessing, Khalid Abdelaziz and Hereward Holland; Writing by Ulf Laessing; Editing by Andrew Osborn)