The fighting will frustrate international mediators who had pressured both sides to stop the ethnic-fuelled conflict.
A UN official confirmed there had been fighting in the area of the flashpoint town of Bentiu, saying shooting came from both sides. Both army and rebels reported clashes elsewhere.
President Salva Kiir and rebel commander Riek Machar met face to face on Friday to sign the ceasefire deal - the second time the two sides have promised to stop fighting, after an accord in January swiftly collapsed.
All fighting was supposed to stop 24 hours after the signing late on Friday.
Clashes erupted in December after tensions sparked by Mr Kiir's decision to sack his rival Mr Machar from the post of deputy president.