The United Nations and the United States fear the border clashes, which broke out on Monday, could escalate and re-ignite a civil war between the mainly Muslim north and the South where most adhere to Christian and animist beliefs.
Sudan said South Sudan's army had attacked the Sudan side of the disputed Heglig oil field area, the scene of several clashes in the past days, state news agency SUNA said.
"The (Sudanese) armed forces are now dealing with the enemy forces," army spokesman Sawarmi Khalid Saad told SUNA.
There was no immediate response from South Sudan, which accused Khartoum of having bombed two areas on the oil-producing southern side of the border.
"The government of Sudan attacked Manga today at two in the morning," Pagan Amum, head of South Sudan's negotiating team, told reporters in Addis Ababa, where the African Union is trying to restart talks between the neighbors.
"Panakuach, also in Unity State, has been subjected to aerial bombardment today, including attacks by helicopter gunship," he said. "As we speak, Sudan is bombing South Sudan."
Sudan's army spokesman denied the allegation.
South Sudan became independent from Khartoum under a 2005 peace agreement that ended decades of civil war that killed 2 million people.
Both sides were supposed to resume talks this weekend but African Union officials said key members of Sudan's delegation, such as its defense minister and the chief-of-staff of its army, had yet to arrive.
Sudan's delegation said it was committed to talks as Khartoum wanted peace, without giving a time frame.
"The government confirms that dialogue with South Sudan is the right way to solve all issues and to have peace between the two states," the delegation said in a statement, SUNA reported.
Amum accused Khartoum of trying to delay the talks.
"The government of Sudan did not send the leader of their team. It is now clear that they have different intentions," he said.
As well as agreeing a halt to further hostilities, the two sides need to decide how much the landlocked South must pay to export its crude oil through Sudan. Juba has shut down its entire oil production to stop Khartoum taking oil as compensation for what it calls unpaid transit fees.
Both countries have yet to mark the 1,800 km (1,200 mile)border, much of which is disputed, or found a solution to the disputed border region of Abyei. Both sides also continue to accuse one another of supporting rebels on each other's territory.
(Writing by Ulf Laessing; Editing by Alison Williams)
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