Southern Sudan announced Sunday that 99 percent of voters in the south voted for independence during a referendum earlier in January.
But Kiir said Monday that the contested region of Abyei needs to also hold a referendum or be given to the south. The status of region is being decided by north-south negotiations.
Kiir spoke during an African Union summit in Ethiopia's capital.
Southern Sudan is slated to become the world's newest country in July. The independence referendum was guaranteed in a 2005 peace accord that ended a more than two decade north-south civil war.