The Bank's board denied his claims that its ethics committee had approved the promotion of Shaha Riza.
Concerns that the scandal will hinder the World Bank's efforts to chide developing nations away from corrupt practices have been brushed off by Mr Wolfowitz, who has apologised for making a mistake over the issue.
Now at least 32 members of the institution's anti-corruption group have handed a letter to its board. They claim they cannot continue their efforts with Mr Wolfowitz remaining in place.
"As is known, there are reports from the field offices of concrete cases where the bank's policy dialogue and operational work on governance and anti-corruption are being undermined," the Reuters news agency quoted the letter as saying.
"The credibility of our frontline staff is eroding in the face of legitimate questions from our clients about the bank's ability to 'practice what it preaches' on governance."
Mr Wolfowitz was appointed to head the World Bank in 2005. Its board is currently considering whether or not he should continue in this role.
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