Fighting raged in the oil-producing state of Upper Nile, Defence Minister Kuol Manyang told AFP, adding that government troops had been ordered "not to go and attack, but only to fight in self defence."
Since President Salva Kiir and rebel leader Riek Machar signed a deal Friday to halt fighting, both sides have accused each other of launching ground attacks and artillery barrages against each other.
Machar was "not in control of his forces" and heavily armed militia troops known as the White Army -- who smear themselves in wood ash to ward off mosquitoes and as war-paint -- had attacked government troops, Manyang said.
"These are irregular forces, the White Army is armed civilians, and they do not know about the cessation of hostilities agreement that was signed," he added.
"They are the ones that attacked, because they think the war is still going on."
Army spokesman Philip Aguer said that monitors from regional bloc IGAD were being sent to the flashpoint town of Bentiu, capital of the northern oil-producing Unity state, which has swapped hands repeatedly in the conflict.
Kiir has insisted he wanted peace, telling crowds in Juba on Sunday that "we have ordered our forces not to lift a foot from where they are to attack rebels".
The two sides had agreed to a ceasefire in January, but that deal quickly fell apart and unleashed a new round of fierce fighting.
Observers have said both side will face challenges in implementing a truce, with the rebels made up of a loose coalition of army defectors and ethnic rebels.
Both sides accuse the other of using mercenaries and rebel forces from neighbouring Sudan, while on the government side -- backed by Ugandan troops -- the command structure under Kiir is also seen as weak.
The war in the world's youngest nation has claimed thousands -- and possibly tens of thousands -- of lives, with more than 1.2 million people forced to flee their homes.
