“He must act honourably and resign,” the de facto union said in a letter to the World Bank’s 10,000 staff.
Wolfowitz personally ordered the hefty pay rises for Riza, according to a report by The Financial Times published on Thursday.
It cited two people who had seen a memo from Wolfowitz to the head of human resources spelling out the terms of the package.
Wolfowitz said: “This was not in any way to protect personal interests. My real regret was that I didn’t more forcefully keep myself out of it.
“I take full responsibility for the details of the agreement,” he said, after saying that he had followed advice given by the bank’s ethics committee on the employment of Riza.
Colin Bradford, research professor in economics and international relations at the Brookings Institution, told Al Jazeera: “The fact is that there’s evidence that he directly intervened in the matter and made some decision or recommendations that amount to decisions on his case on how to handle it.
“It takes absolutely no brains whatsoever that it is utterly and totally inconsistent with the message of anti-corruption and good governance, which the bank is trying to promote.”
Riza was transferred from the World Bank’s communications office to the US state department in line with bank regulations to avoid a conflict of interest after Wolfowitz’s appointment in mid-2005.
While still on the World Bank payroll, she was rapidly promoted and given large salary increases.
Wolfowitz acknowledged that the situation surrounding Riza “had the potential to harm this institution” and said that given his romantic involvement with her, he faced a “painful personal dilemma when I was new to the institution”.