The peace conference was one of the key decisions taken by the Abyei Joint Oversight Committee (AJOC) on its first extraordinary meeting on May 2 and 3 in Abyei.
The meeting took place days before Ngok Dinka paramount chief Kuol Deng Kuol was killed by Misseriya nomads together with an Ethiopian peacekeeper.
AJOC urged all Abyei communities to exercise maximum restraint and desist from acts or making any inflammatory statements that may lead to violent clashes.
The committee also declared Abyei a weapons-free area and appealed to the Governments of South Sudan and Sudan to form quickly both the Abyei Area Council and Administration.