The ceasefire formally began at 1730 GMT on Friday, well after dark in South Sudan.
The United Nations reported "sporadic fighting" before and after the deadline, UN deputy spokesman Farhan Haq said.
Rebel spokesman Lul Ruai Koang said before the ceasefire deadline that the army had attacked positions in the northern oil state of Unity, and in the volatile eastern Jonglei region.
Koang alleged that South Sudanese government troops -- as well as Ugandan soldiers and rebels from neighbouring Sudan's war-torn Darfur region, the Justice and Equality Movement (JEM) -- had attacked rebel positions on Friday.
Army spokesman Philip Aguer in turn accused the rebels of launching attacks Friday afternoon in Jonglei, but said the government force had beaten back the assault, and that fighting was over before the ceasefire deadline.
Saturday morning, in the first hours of daylight of the ceasefire, Aguer said the clashes appeared to have ended.
"There are no reports of fighting, it is calm," he said.
It was not possible Saturday to immediately contact rebel forces, and gathering reports from across the vast and remote regions of South Sudan -- large areas of which have poor if any telephone network -- is a difficult task.
Both sides pledged on Thursday to end five weeks of bitter conflict, but both sides have said they doubt the other can fully control the forces on the ground.
The ceasefire agreement was signed late Thursday in the Ethiopian capital Addis Ababa by representatives of South Sudan's President Salva Kiir and rebel delegates loyal to ousted vice president Riek Machar.
Up to 10,000 people are believed to have been killed in the fighting pitting forces loyal to Kiir against a loose coalition of army defectors and ethnic militia nominally headed by Machar, a seasoned guerrilla fighter.
The fighting has been marked by atrocities on both sides with some 700,000 people forced from their homes in the impoverished nation, according to the United Nations.