Colonel Philip Aguer said on Friday that the bombs were dropped late Thursday afternoon. He said two civilians were wounded in the bombings, which took place on the town of Laloba, about 50 kilometres north of the Unity State capital of Bentiu in South Sudan.
The attacks came one day after Sudan announced it had accepted an agreement put forward by the African Union to return to talks with South Sudan. The agreement demands both sides adhere to a ceasefire.
Violence between the two sides has flared in recent weeks, pushing the region to the edge of an all-out war.
