"The ambulance was called immediately and arrived within five minutes. Allegations that he was dying in front of police do not correspond to reality," the Estonian State Prosecutor's office said.
Earlier Friday, Russian President Vladimir Putin demanded punishment for those guilty of failing to save the life of Dmitry Ganin.
"It is not the case that that an accident occurred. We are worried that this person was not given aid when he was injured. He was dying in front of police. This is a deliberate crime, and we demand that the criminals be brought to account," he told journalists after a Russia-EU summit near the Volga city of Samara.
Estonian police detained May 11 two people suspected of killing Ganin, and beating his friend Oleg. Prosecutors issued Sunday an arrest warrant for a six-month term. No murder charges have been brought yet.