Speaking at an hours-long press conference, Zelenskiy said Ukrainian intelligence had obtained audio recordings of the plotters, including people from Russia, trying to rope business magnate Rinat Akhmetov into joining a coup.
The Kremlin swiftly denied any role in any coup plot, saying it had no plans to take part in such acts. A spokesperson for Akhmetov, Ukraine's richest man, had no immediate comment.
Zelenskiy was speaking amid rocketing tensions between Ukraine and Russia that have raised fears that a simmering conflict between Ukraine and Russian-backed separatists could escalate into open war between the two neighbors.
Ukraine's sovereign dollar bonds tumbled to their lowest in more than a year on Friday and the cost of insuring exposure to the country's debt soared amid rising security concerns.
Zelenskiy did not give full details of the coup plot. Asked explicitly whether he thought the Kremlin was involved, he said: "I'm sorry, I can't talk about it."
But he also spoke at length at the press conference of a threat of Russian military escalation, and said Ukraine would be ready for it.