A Ukranian spokesman says 2 civilians have been killed since the ceasefire came into effect overnight.
A military official said Ukranian positions have been shelled by rebels ten times since the midnight deadline for a cessation of violence.
Both sides ordered their forces to stop fighting from midnight local time (22:00 GMT Saturday).
Shortly after the ceasefire began overnight, Ukraine's President Petro Poroshenko insisted his fighters would keep their promise:
