MOSCOW — The strange cast of characters emerging in the faked assassination of a prominent Putin critic — including a Russia-hating right-wing priest and the director of a Ukrainian arms manufacturer — set the already bizarre case on a path to a murky, up-is-down mess of the sort that Ukraine seems to specialize in.

Both the priest and the executive claimed to be working for Ukraine’s intelligence services. Ukrainian officials at first denied that but, in the case of the priest, subsequently reversed themselves and admitted he had played a role. They would not say what.

Senior Ukrainian officials have been on the defensive since Wednesday, when the head of the security services and the chief prosecutor announced that they had staged the shooting death of a dissident Russian war correspondent in order to trace his would-be killers back to Russian intelligence.

However, in the absence of solid facts and real evidence about any plot to kill the dissident, Arkady Babchenko, somewhat implausible figures have emerged from the shadows, perhaps the most unlikely being the priest, who claimed he was hired to carry out the hit.