Kiir and Sudan's Omar Hassan al-Bashir agreed in September to withdraw troops from the disputed border as a precondition to resume oil exports from landlocked South Sudan through Sudan. Oil revenues are vital to both economies.
But both countries still have troops 10km from each other's border, and both accuse each other of supporting rebels on the other's territory.
Kiir and Bashir are scheduled to meet this month at a summit brokered by the African Union to discuss how to set up the border zone, which will be monitored by soldiers from both sides and UN peacekeepers.
"To be able to establish the border monitoring mission, we are temporarily withdrawing our forces from the immediate border areas," Kiir said in a speech on New Year's Eve.
"This will allow for a demilitarised border zone to be operational," he said without giving a date for the pullout.