Poroshenko told relatives of those killed that Kiev's security service had testimonies from Ukrainian law enforcement officials saying top Kremlin aide Vladislav Surkov organised "groups of snipers" during the protests, a statement from the presidency said.
Poroshenko said that investigators had recordings of conversations between then-president Viktor Yanukovych and Russian security officials "in which they prepared the shooting of activists in advance," the statement said.
Moscow immediately dismissed the allegations, with foreign ministry spokesman Alexander Lukashevich labelling them "ravings, worthy of a psychiatric hospital".
Public anger is high in Kiev over the fact that no officials have yet been brought to justice for the killings of the protesters.
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Low-ranking riot police are the only people currently awaiting trial over the shootings.
Ukraine accuses Yanukovych - now living in exile in Russia - of ultimately being responsible for the protesters' deaths.
Surkov is an influential Kremlin adviser who has been credited with constructing the system of "managed democracy" that has helped President Vladimir Putin cement his control over Russia.