Idle played a major role in adapting the classic film Monty Python and the Holy Grail for the stage in Spamalot, which earned three Tony Awards and spawned touring productions.
Cleese provided some pre-recorded narration for Spamalot, but Idle recently claimed that he has prevented his former colleague from being more creatively involved in the play.
"I fired John Cleese - surgically removed him. It wasn't mean - he's had millions of dollars from it," The Daily Telegraph quotes Idle as saying. "He charges people a fortune for using his voice. He's always been in financial crisis."
Idle added: "His ex wife was married to him for 20 years. I wouldn't take £13m ($20.2m) to be married to him. I don't feel guilty. I gave him a million dollars. Has he sent me a Christmas card? No, he's too busy on the road."
Cleese took to Twitter to dispute Idle's claims that he made millions off Spamalot and accused his fellow Monty Python member of hoarding the profits.
"I see Yoko Idle's been moaning (again), about the royalties he had to pay the other Python's for Spamalot. Apparently he paid me "millions" (sic)," Cleese tweeted.
The comic added: "Actual rough figures last time we checked - Yoko Idle $13m, Michael Palin $1.1m, the others just under a million each."
Cleese recently joined up with Monty Python's Palin, Terry Jones and Terry Gilliam to record dialogue for the late Graham Chapman biopic A Liar's Autobiography, but Idle did not take part.
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Watch a clip from the Broadway production of Spamalot below: