Ukrainian President Petro Poroshenko has reportedly asked the government troops to stop fighting, saying that a truce deal agreed with pro-Russian rebels in the east must be honoured.
Poroshenko also cautioned the separatists against continuing attacks on the besieged strategic town of Debaltseve, reported the BBC.
Fighting appeared to have died down immediately after the ceasefire took effect at midnight on Saturday.
However, both government and separatists accused each other of violating the ceasefire in some places.
The rebel leaders had also ordered their forces to stop fighting and respect the ceasefire earlier on Saturday.
More than 5,400 people have been killed in the conflict that began in eastern Ukraine in April but the United Nations says that the actual death toll could be much higher.