The demand by the European Union's legislature that the development chief step down comes as a special bank panel is probing whether Wolfowitz violated bank rules in his handling of the 2005 promotion of bank employee Shaha Riza to a high-paying State Department job.
The World Bank's 24-member board will ultimately decide what action, if any, to take.
Many of the bank's staff, former World Bank executives, aid groups and some Democratic politicians have pressed for Wolfowitz to resign. They fear the matter has tarnished the reputation of the institution, which is focused on fighting global poverty, and could hobble efforts to raise billions of dollars for a World Bank program to help poor countries.
The EU assembly said it wanted to "signal to ... Wolfowitz that his withdrawal would be a welcome step toward preventing the bank's anticorruption policy from being undermined."
Wolfowitz has acknowledged making a mistake and apologized, but he has said he won't quit.
At the White House on Wednesday, President Bush took care to offer a positive mention of Wolfowitz at an event to mark Malaria Awareness Day. Wolfowitz was seen there, chatting enthusiastically with other attendees.
"I appreciate very much the fact that the World Bank is taking the lead in eradicating poverty in places like Africa, and Paul Wolfowitz, thank you for your leadership of the World Bank," Bush said.
The United States the bank's largest shareholder has expressed confidence in Wolfowitz, and some African and Asian representatives have also indicated some support.
Hoping to repair relations with staff and boost morale, Wolfowitz said Tuesday he'll make "major changes" in the way his office and the senior management team work to address the concerns.