Green had attempted to prosecute the pair over the broadcast and tour of 'Jerry Springer the Opera', accusing them of blasphemy. However, the case was thrown out of the High Court last December and a fortnight ago Green was ordered to pay costs of £90,000.
Green has said he will "certainly end up bankrupt" if forced to pay the money, and is now urging Thompson and Thoday, whose company Avalon produced the show, to waive their costs "in the interests of goodwill and justice".
He said: "Mark Thompson earns well over 20 times as much in a year as I am worth. He could pay his own costs out of his inflated salary, and the BBC certainly would never notice the odd £55,000 alongside the money they squander on a daily basis.
"Jonathan Thoday can easily afford to waive his costs as well. He lost £500,000 over the failed tour of 'Jerry Springer the Opera' in 2006, and didn't bat an eyelid, so he isn't exactly short of money either."
A BBC spokesperson said: "While we will look at this request, it is important to remember it was Mr Green who chose to seek to bring a private prosecution for a criminal offence.
"We always believed the case had no merit and should never have been brought but clearly had no choice but to defend against it. It is regrettable that the BBC was forced to spend considerable public money doing so."
Thoday, joint managing director of Avalon Group, said: "The actual legal costs incurred were far higher -- this was a settlement figure put forward by Stephen Green's legal representatives and it was accepted in good faith."
Green has set up a for supporters to sign, backing his request for a reprieve. However, a has also been set up from people who want the BBC and Thoday to pursue their right to the payments.
'Jerry Springer the Opera' started life as a fringe theatre show, written by Richard Thomas and Stewart Lee. It became a cult hit after an initial run at the Battersea Arts Centre, and ended up as a production at the National Theatre before transferring to London's West End.
Plans to broadcast the show on BBC Two in January 2005 ran into trouble with Christian fundamentalists, who objected to its portrayal of Jesus, including scenes where he wore a nappy and declared himself to be "slightly gay".
The BBC went ahead with the broadcast despite 55,000 complaints. However, it effectively ended the life of the show because plans for a national tour had to be cut back after threats against theatre owners.
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