The African Union has called on Sudan to stop its aerial bombing of South Sudan and expressed "dismay and deep disappointment" with both countries for their involvement in the hostilities.

In a statement released after a council meeting on Tuesday, the AU said Sudan and South Sudan must withdraw their forces from the disputed border region and keep their troops within their borders - and stop issuing "hostile propaganda and inflammatory statements" that could escalate the conflict.

Although neither side has declared war, the President of South Salva Kiir earlier said that Sudan had "declared war" on his country after the north's repeated bombing of the south.

South Sudanese government officials in Unity State accuse Sudan of ignoring the recent calls by the international community to end the border conflict between the two nations, by attacking two towns in Unity State, killing two and injuring six people, the Sudan Tribune reported.

Sudanese President Omar al-Bashir has made it clear that there will no talks with the South, calling them "poisonous insects", for challenging Sudan's claim to a disputed territory near the border.

The AU said South Sudan and Sudan must resume negotiations, which collapsed early in April in Ethiopia when the two countries started attacking each other.