Rebels of the Justice and Equality Movement (JEM), from the western region of Darfur, combined with insurgents from the Sudan People's Liberation Movement-North (SPLM-N), which for several months has been fighting in South Kordofan and Blue Nile states along the border with breakaway South Sudan, said JEM spokesman Gibril Adam Bilal.
Last November, the two rebel groups joined with factions of Darfur's Sudan Liberation Army to form the front dedicated to "popular uprising and armed rebellion" against the National Congress Party government in Khartoum.
"This attack is under the umbrella of the Sudanese Revolutionary Front," Adam told AFP.
He said Sunday's offensive happened at Jau, a disputed area on the poorly defined north-south border.
Sudan Armed Forces spokesman Sawarmi Khaled Saad confirmed that the area had come under attack but he blamed the forces of South Sudan.
"This attack was completely planned and sponsored by the government of South Sudan," he said.
"The fighting is going on now."
Neither side could immediately give casualty figures.
South Sudan split from Sudan in July last year after an overwhelming vote for independence following more than two decades of war that killed two million people.
Border tensions have since flared, with each side accusing the other of supporting rebels within its territory, while a major dispute over oil transit fees remains unresolved.
UN Secretary General Ban Ki-moon has warned that the crisis between the neighbours has become a major threat to regional peace and security, and Britain this month expressed "grave concern at the recent build-up of forces and escalation of tensions in conflict-affected border areas."
The ethnic minority insurgents from the SPLM-N had previously fought alongside the former rebels now ruling in the South.