The two former civil war foes have accused each other of provoking the clashes in the disputed area around Sudan's South Kordofan border state. South Sudan, which declared independence in July, has been locked in a dispute with Khartoum over oil payments and other issues.
Sudanese rebels said the Khartoum government was carrying out air and ground attacks in South Kordofan on Wednesday. Sudan's military spokesman could not immediately be reached for comment.
South Sudan's army (SPLA) said it had repulsed an attack on Tuesday and pursued Sudanese troops into the disputed Heglig area, vital to Sudan's economy because it has an oil field that accounts for about half of its 115,000 barrel-a-day output.
But Khartoum said it was an aggression.
"On Tuesday morning and afternoon, areas of South Kordofan state, most notably Heglig, were brutally attacked by the SPLA, supported by the state of South Sudan, using mercenary forces and rebel groups," Sudan's Information Ministry said in a statement.
"The government of Sudan announces it will oppose this flagrantly aggressive behavior by all legitimate ways and means."
Al Jazeera television on Tuesday quoted a government source in Khartoum as saying South Sudan's army had taken control of the Heglig oil area, but South Sudan's military spokesman Philip Aguer said he could not confirm the report.
He was not immediately available to comment on Wednesday.
The South Kordofan state has seen an insurgency since June by rebels who had fought as part of the southern rebel Sudan People's Liberation Army during the civil war.
Fighting spread to the nearby Blue Nile state in September.
When Sudan was partitioned under a 2005 peace deal that ended the civil war, tens of thousands of fighters who had sided with the south were left north of the border. Sudan accuses Juba of continuing to back the insurgents, which South Sudan denies.
The rebels, renamed the SPLA-North, said they were fighting government forces in the villages of Toma and Hassan, about 45 km (28 miles) west of Rashad town, on Wednesday.
"The Sudanese army is using air strikes, and there is fighting on the ground," SPLA-N spokesman Arnu Lodi said.
Violence in the border regions has hampered negotiations over partition-related issues including demarcating the border, determining the status of citizens in one another's territory and dividing up debt.
Importantly, the two still need to work out how much landlocked South Sudan - which took about three quarters of what was the united country's oil output when it seceded - should pay to export crude using pipelines and other infrastructure in Sudan.
South Sudan shut down its output of about 350,000 barrels a day in January after Khartoum started taking some oil to make up for what it called unpaid fees. Oil accounted for about 98 percent of South Sudan's state revenues.
About 2 million people died in Sudan's civil war, waged for decades over ideology, ethnicity, religion and oil.
(Reporting by Alexander Dziadosz and Khalid Abdelaziz; Editing by Alessandra Rizzo)
(This story was corrected to say in paragraph 3 that rebels say Khartoum is carrying out strikes, not S.Sudan)
Reuters