Spokesmen for both the government and the pro-Russian rebels said some shelling had continued, mainly around the besieged town of Debaltseve.
But both sides say the truce that came into force at midnight (22:00 GMT Saturday) is holding with some exceptions.
OSCE monitors agree, but complain they have been denied access to Debaltseve.
The town – a key transport hub – has been the object of some of the fiercest fighting in the conflict zone in recent weeks, and the ongoing struggle there appears to pose the gravest threat to the truce.
Analysts point out that previous ceasefires initially appeared to be holding but eventually failed, and say the next 48 hours are critical.
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.
Ukrainian President Petro Poroshenko, Russian President Vladimir Putin, French President Francois Hollande and German Chancellor Angela Merkel brokered the agreement on Thursday after lengthy talks in the Belarusian capital Minsk.
President Poroshenko has warned that Ukraine will not “turn the other cheek” if the deal is violated.
In a televised address at the time the ceasefire took hold, he said Ukrainian troops in Debaltseve had been resupplied with ammunition.
Two rebels commanders, meanwhile, have been quoted as saying they are entitled to open fire in Debaltseve, with one reportedly saying it was “their territory” and the ceasefire only applied to the frontline.
The US, which has warned it could begin supplying arms to Ukraine if the peace initiative failed, claimed on Saturday it had evidence that the Russian military had deployed weaponry around Debaltseve – contrary to Moscow denials that it is playing any direct role in the conflict.
Ertugrul Apakan, head of the Organisation for Security and Co-operation in Europe (OSCE) monitoring mission, said in a briefing that the ceasefire mainly held in the first 12 hours – with some exceptions including Debaltseve and Luhansk.
But, referring to the denial of access to Debaltseve, he called on rebels to allow safe entry to all areas for monitors.
On Sunday morning, Ukraine military spokesman Vladyslav Seleznyov said the truce was being “observed in general”.
Another spokesman, Anatoly Stelmakh, said there had been some 10 incidents of shelling since the truce took hold, mainly around Debaltseve.
He said Ukrainian forces had “repelled a few attacks” in Shyrokyne, near the strategic southern port city of Mariupol.
He claimed hundreds of “terrorists” had been killed in the previous two days.
A rebel spokesman, Eduard Basurin, concurred that the truce was largely holding for the time being but complained that Ukrainian forces were continuing to shell Debaltseve.
Reports from the main rebel stronghold of Donetsk said the city had suddenly fallen silent, allowing residents in the city some precious respite from artillery bombardment.
But few residents expressed confidence that the truce would hold for longer than a few days.
According to the Minsk agreement, cessation of hostilities is only the first step and should be followed by the creation of two demilitarised buffer zones between 50-140km (30-85 miles) wide, beginning on Monday.
European leaders have warned Russia that it could face additional sanctions if the 13-point ceasefire agreement is not respected.