Once the new deal has been established, southern ministers who quit the national unity government in Khartoum on September 11 in protest at delayed implementation of the agreement will resume their positions, Piong said.
"We want this return [to the government] to be made at a ceremony which will mark the relaunch of implementation of the Comprehensive Peace Agreement."
Disputed oil district
Kiir had expressed his optimism about an imminent breakthrough in the crisis between the two parties, but he said that the issue of the disputed oil district of Abyei is still the subject of negotiation.
Piong said that the final borders between north and south was the only other unresolved issue between the sides.
A recommendation on Thursday by the Ceasefire Political Committee, which is made up of military commanders from both sides, to move the deadline for northern troops withdrawing from the south to December 15 was endorsed by Bashir and Kiir.
The Sudanese military originally had a July 9 deadline to withdraw, as set in the 2005 agreement.
Southern former rebels say 17,6000 Sudanese troops remain in the south, although the military says they number 3,600.
The SPLA also maintains about 5,000 troops in the north. The peace deal states they should be redeployed to the south.