After a controversial draw in their first meeting two years ago, Fury ended Wilder's reign as world champion with a seventh-round stoppage over the American, who had bicep surgery after the first defeat of his career in February.
It was widely anticipated the pair would complete their trilogy of fights on December 19 but Fury said he had "moved on" after claiming Wilder and his team were trying to push the contest back to next year.
Fury has since announced a homecoming fight in London on December 5, with Carlos Takam, who lost to Anthony Joshua in 2017, and former European heavyweight champion Agit Kabayel rumoured to be among the preferred opponents.
Wilder has largely kept his counsel since losing to the unbeaten Fury but broke his silence on his social channels on Saturday evening.
He wrote: "Fury @gypsyking101 it is time for you to be a man and honor (sic) your agreement.
"What is this b******t of you fighting Carlos Takam instead of me, you got to be kidding.
"When you were going through your darkest time, I told you that if you got yourself together I would give you a title shot. Being a man of my word, I gave you the title shot.
"When that fight was a draw, I told you that I would give you a rematch. You know I was offered more money to fight Joshua than I was getting to fight you. Again being a man of my word, I fought you like I said I would.
"In the rematch agreement, there was a rematch clause. Now it is time for you to be a man and honor your word, instead of trying to weasel out of our agreement.
"Scared people run but a scary man will break his contract you coward."