The ceasefire, which started at midnight local time (2100 GMT yesterday), was agreed at a meeting with the separatists and the Contact Group for Ukraine, consisting of representatives from Kiev, Moscow and the Organisation for Security and Co-operation in Europe (OSCE).
The halt to the fighting is intended to allow local farmers to harvest their crops and is set to last until August 31.
But "despite the ceasefire accords starting today," two Ukrainian soldiers were killed and two others wounded , the army said in a message published on Facebook.
On the other hand, representatives of the self-declared rebel Donetsk republic (DNR) claimed there were around 10 violations of the ceasefire by the Kiev forces, firing on rebel positions with "artillery, mortars and tanks."
"All the information on these violations (of the ceasefire)... Have been sent to the OSCE," said DNR representative Edouard Bassourine, according to Russia's Interfax news agency.
So far, none of the truces declared during the two-year conflict has lasted.
The OSCE, which runs a monitoring mission in the conflict zone, regularly reported violations of the last truce over Easter.
Russia's President Vladimir Putin on Saturday paid a visit to the Black Sea peninsula which Moscow annexed in 2014, triggering protest from Kiev saying the Russian strongman was violating Ukraine's sovereignty.
The fighting in the pro-Russian insurgency in eastern Ukraine, which Kiev and its Western allies say is backed by Moscow, has claimed more than 10,000 lives since the start of the conflict.
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