"We call upon holders of arms abroad and leaders and governments of neighboring countries which seek to disturb the security and stability in the Sudan to reconsider their position," National Congress Party secretary general Ibrahim Ahmed Omar was quoting as saying by the official SUNA news agency.
He described as "backward" the motives of the Beja Congress and Free Lions Movement that form the Eritrea-based Eastern Front, which charges that the eastern region has been neglected by the Arab-dominated regime in Khartoum.
Omar said power-sharing "is an issue that should be considered in frankness and objectivity."
NCP political secretary Majzub Ahmed called on the eastern rebels to lay down their arms and "resort to peaceful means for resolving problems."
The veiled overtures came on the heels of landmark meeting between Sudanese President Omar al-Beshir and Isaias Afeworki of Eritrea in Libya last week -- their first encounter in years.
The two are bitter enemies that have long accused each other of providing sanctuary and support to opposition groups.