"You still have the opportunity to avoid long-term damage by resolving this matter in a fair and equitable way that recognises that we all tried to do the right thing, however imperfectly we went about it," he said.
The controversy arose after it was revealed Wolfowitz had agreed a large pay deal for Shaha Riza, a World Bank Middle East expert and Wolfowitz's companion, who was made to move to the US state department when Wolfowitz took over at the bank.
"I have been caricatured as a 'boyfriend' who used his position of power to help his 'girlfriend'," he said.
Promise to change
Wolfowitz was addressing the board on Tuesday in a last attempt to explain his actions. The board must now considered whether he should stay, resign or be fired for his actions.
"Wolfowitz must resign because... his act of favouritism for personal interest was wrong"
Ibby, Mumbai, India
Send us your views
He said his decisions at the time were made in the best interest of the institution.
"Ms Riza's external placement does not justify taking any action against me or warrant a finding that you lack confidence in my leadership," he said.
In his plea to the board, Wolfowitz, a former deputy US defence secretary who played a high-profile role in planning the US invasion of Iraq, also said it had become clear to him that the controversy had more to do with his management style and policies than the Riza scandal.
He said he had acknowledged publicly and in meetings with staff that he needed to make changes and had relied too long on advisers he brought with him from the Pentagon and White House instead of the advice of career staffers.
"I realised even before this crisis that change in this regard was overdue and I intend to make it, and make it decisively," he said, promising to open up direct channels of communication between himself and the bank's senior management.