The ceasefire came into effect at 1730 GMT despite rebel accusations that the army had attacked their positions in two separate regions just hours earlier.
"The UN Mission in South Sudan says that sporadic fighting took place in parts of the country today," including after the ceasefire, UN deputy spokesman Farhan Haq said.
Rebel spokesman Lul Ruai Koang said before the ceasefire deadline that "simultaneous attacks have been launched" by the army on positions in the northern oil state of Unity, and in the volatile eastern Jonglei region.
Both sides pledged yesterday to halt fighting within 24 hours and end five weeks of bitter conflict that has left thousands dead, but both sides have said they doubt the other can fully control the forces on the ground.
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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, warning they had the "right to defend themselves against this senseless aggression."
"It is critical that both parties implement the cessation of hostilities agreement in full and immediately," the UN spokesman said.
US President Barack Obama, whose country provided crucial backing on South Sudan's path to statehood, described the deal as "a critical first step toward building a lasting peace".
Kiir urged those rebels not under Machar's control to also respect the deal.
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.