Col. Philip Aguer, a spokesman for the Sudan People's Liberation Army of South Sudan, said that the aerial strike hit a market area in Rubkona, which is part of Unity state, at 1 p.m. Saturday (6 a.m. ET).
Abiemnom County in that state, as well as two counties in Warrap state, were also attacked Saturday, Aguer said.
But Al-Sawarmi Khalid, a spokesman for the Sudanese Armed Forces, said, "We have not carried out attacks into South Sudan."
Both military spokesmen referenced Heglig, a key oil installation in South Kordofan state that produces nearly half of Sudan's oil and was seized by South Sudan's military this week.
Aguer insisted Heglig is part of South Sudan.
Meanwhile, Khalid said that Sudanese military forces were "approaching Heglig from all sides."
Sudan's ambassador to the United Nations welcomed a U.N. Security Council statement this week demanding "a complete, immediate and unconditional end to all fighting and a withdrawal of the SPLA from Heglig and an end to aerial bombardments."
"We will observe closely the behavior and attitude of the reaction of the government of the South to this call and if they don't heed it, we will reserve our right to exercise the right of self-defense and we will chase them out, " Ambassador Daffa-Alla Elhag Ali Osman said.
The European Union's foreign policy chief, Catherine Ashton, has called South Sudan's move to occupy Heglig "completely unacceptable" and urged forces to withdraw immediately. The African Union similarly has called on forces to pull out and for aerial bombardments to stop.
Yet South Sudan's ambassador to the United Nations blamed the Khartoum government for attacks on their forces at the border, which she said provoked their actions at Heglig.
"South Sudan had no choice. It had to defend itself to deter attacks on South Sudanese territory," Agnes Oswaha said. "South Sudan is prepared to withdraw troops as long as a mechanism is put in place that the area cannot be used to launch further attacks."
South Sudan gained independence from the north in July, the result of a referendum overwhelmingly approved by voters last year.
The referendum was part of a 2005 peace deal that ended decades of civil war between the two sides that killed about 2 million people.
Despite the split, several outstanding issues have yet to be negotiated, including citizenship, border demarcations and oil revenue sharing.
When they separated, South Sudan acquired three-quarters of Sudan's oil reserves. The two countries have been locked in negotiations over how much the landlocked South Sudan should pay to use a pipeline and processing facilities in the north.
In late July, South Sudan halted oil production after accusing Sudan of "stealing" $815 million worth of its crude. Sudan said it confiscated the oil to make up for unpaid fees.
