They said the WBC, whose title Wilder holds, was forced to call off the fight only after Wilder threw "the equivalent of a childish temper tantrum" and decided not to fly to Russia.
Wilder then began a public "smear campaign" against Povetkin and Ryabinskiy, the lawsuit said.
Povetkin and World of Boxing are seeking at least $34.5 million for the alleged breach of contract and defamation.
The lawsuit was filed 10 days after Wilder and DiBella filed their own $5 million breach of contract lawsuit against Povetkin and World of Boxing, saying the Russian's April 27 positive test forced the fight's cancellation.
Both lawsuits were filed with the U.S. District Court in Manhattan.
Judd Burstein, a lawyer for Wilder and DiBella, in an interview said the countersuit was "absurd," and that Povetkin "would be better off to just stop doping, and fight clean."
The World Anti-Doping Agency added meldonium to its banned substances list on January 1.
Tennis star Maria Sharapova is appealing her own two-year ban after she tested positive for meldonium.
Wilder is scheduled to defend his title against Chris Arreola on July 16 in Birmingham, Alabama.
The cases are World of Boxing LLC et al v. Wilder et al, U.S. District Court, Southern District of New York, No. 16-04870; and Wilder et al v. World of Boxing LLC et al in the same court, No. 16-04423.
(Reporting by Jonathan Stempel in New York; Editing by Frank Pingue)
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