Senior government officials told the Sudan Tribune the Khartoum-backed rebels have refused calls for a peaceful settlement and have instead been stocking up on ammunition and weapons.
The operation follows the killing in February of 104 migrating civilians and 14 soldiers by rebels loyal to David Yauyau in Akobo County.
Joshua Konyi, Pibor County commissioner, said fierce fighting took place Monday with heavy casualties inflicted on the rebels.
Konyi said Murle civilians have been urged to leave their rural villages and move into towns until the rebels have been defeated.
Clashes between the army and forces loyal to David Yauyau began after he lost a 2010 election for a seat in parliament.