Both sides ordered their forces to stop fighting from midnight local time.
However, they later traded accusations over reported artillery and mortar fire.
Fighting had raged near the besieged strategic town Debaltseve just hours before the truce, agreed by leaders this week in Minsk, was due to kick in.
Ukrainian President Petro Poroshenko, Russian President Vladimir Putin, French President Francois Hollande and German Chancellor Angela Merkel brokered the agreement on February 12 after marathon talks in the Belarusian capital.
Officials say more than 5,400 people have been killed since the conflict erupted in eastern Ukraine in April, but the UN believes the actual death toll to be much higher.
The fighting followed the annexation by Russia of Ukraine’s southern Crimea peninsula.
Ukraine and the West accuse Russia of sending troops and weapons to help the separatists in Ukraine’s eastern Donetsk and Luhansk regions – a claim the Kremlin vehemently denies.
Ukrainian military spokesman Vladyslav Seleznyov said army positions in the town of Popasna and near the villages of Zolote and Chernukhyno were fired on after the ceasefire.
Meanwhile, senior rebel defense official Eduard Basurin said Ukrainian forces in Debaltseve fired on rebels positions, prompting them to return fire.
Just before midnight, President Petro Poroshenko ordered the commander of what Ukraine describes as its “anti-terror operation” to observe the ceasefire.
In a national broadcast from the military headquarters in Kiev, Petro Poroshenko expressed hopes that “perhaps the last chance [for peace] won’t be lost”, adding that agreements “must be honored, and we are expecting that the ceasefire deal will be adhered to”.
The president said there was still “alarm” over the situation around Debaltseve, a transport hub where several thousand Ukrainian troops have been besieged by the separatists for days.
The rebels say they have completely cut off supply routes to Debaltseve, encircling the town. Ukraine denies the claim.
Donetsk rebel leader Alexander Zakharchenko said earlier on Saturday that he considered the Debaltseve area was not covered by the agreed ceasefire.
European leaders have warned Russia that it could face additional sanctions if the 13-point ceasefire agreement is not respected.
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