The board was set to resume deliberations Thursday.
Wolfowitz and the Bush administration were seeking a face-saving deal with the board that would allow him to resign under his own terms and escape some blame for the furor involving his girlfriend's compensation.
Pressure on Wolfowitz to step down has grown since Monday's release of a bank panel report on his handling of the 2005 pay package of bank employee Shaha Riza.
Wolfowitz contends he acted in good faith.
European members — led by France, Germany and the Netherlands — are pushing for Wolfowitz to resign. The White House, for the first time, suggested this week that it would be open to a change of leadership.
"It's a game that is still going on. What I understand from people close to the board is that they really want to make a decision on this case because it cannot continue like it is. It's really bad for the bank," said Kees-Jaap Ouwekerk, spokesman for Dutch Overseas Development Minister Bert Koenders.
Behind the scenes negotiations took place on Wednesday for an exit package for Wolfowitz, but they failed to produce a resolution. Wolfowitz and his attorney, Robert Bennett, has said repeatedly that Wolfowitz won't resign with a cloud of what they believe are unfair charges hanging over him.
The 185-nation World Bank, created in 1945 to rebuild Europe after World War II, now provides more than $20 billion a year for projects such as building dams and roads, bolstering education and fighting disease. The bank's centerpiece program today offers interest-free loans to the poorest countries.
By tradition, an American has run the bank, with the board's approval. A European heads the bank's sister agency, the International Monetary Fund.
The United States, the bank's biggest financial contributor, wants to keep that decades-old tradition intact.
Riza worked for the bank before Wolfowitz took over as president in June 2005. She was moved to the State Department to avoid a conflict of interest, but stayed on the bank's payroll.
Her salary went from close to $133,000 to $180,000. With subsequent raises, it eventually rose to $193,590.
The bank panel concluded that the salary increase Riza received "at Mr. Wolfowitz's direction was in excess of the range" allowed under bank rules.
The panel said Wolfowitz "placed himself in a conflict of interest situation" when he became involved in the terms and details of Riza's assignment and pay package and "he should have withdrawn from any decision-making in the matter."
Meanwhile, the German Ministry of Finance said Thursday that Wolfowitz was still expected to attend a meeting of finance officials from the Group of Eight nations in Potsdam on Friday and Saturday, which is supposed to set the agenda for next month's summit of G-8 leaders.
"We did not receive a cancellation," spokesman Torsten Albig said.
There were concerns that the flap over Wolfowitz would overshadow talks on the global economy, which is the main focus on the group. Besides the United States, the countries that make up the G-8 are Britain, Canada, France, Germany, Italy, Japan and Russia.