Sudanese warplanes hit South Sudan's oil-rich border region in a third day of violence between the rival states, as international concern mounted over a return to an all-out war, AFP reported.

Fighting on the ground had reportedly ceased on both sides of the undemarcated border but dead bodies and destroyed tanks lay strewn in Sudan's contested oil centre of Heglig, the site of bloody battles that began Monday, March 26.

Sudanese warplanes launched air raids on newly independent South Sudan, while the rival armies clashed in heavy battles.

Both sides claim the other started the fighting, the worst since South Sudan declared independence from Khartoum last July after decades of civil war.

The African Union and the UN Security Council have called for an end to the violence, while US Secretary of State Hillary Clinton said Khartoum bore the responsibility for the renewed hostilities.

The unrest jeopardises efforts to resolved contentious border and oil disputes that have ratcheted up tensions between Juba and Khartoum. Both sides have said they do not want the clashes to escalate.

Juba said northern bombers and troops had struck first on Monday, moving into Unity State before Southern troops fought back and took the Heglig oil field, parts of which are claimed by both countries. Sudan later retook the field.

Both Heglig -about 15 kilometres (nine miles) from the disputed border's closest point -and Unity state oil fields are run by the Greater Nile Petroleum Operating Company (GNPOC), a consortium led by China's state oil giant CNPC.

More than two million people died in Sudan's 1983-2005 civil war between Khartoum and southern rebels before a peace agreement which led to South Sudan's independence.