The attack was reported on Tuesday evening, it said.
"Militant shells hit private houses on Vosme Bereznia Street in Toretsk's Novhorodske residential area. A young man (born in 1986) was killed in an explosion of a shell near his house," the police said.
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Information about the attack was included in the national register of pre-trial investigations under Article 258 (an act of terror) of the Criminal Code of Ukraine.
The population of Toretsk (formerly Dzerzhynsk, renamed in 2016 under the de-communization law) is about 34,000 people. Late in July 2014, the town was liberated from illegal Russia-backed formations of the self-proclaimed Donetsk People Republic (DPR). Since then, it is regularly shelled by the occupation forces.