“The New York Fed should go back and restart their search now,” said Andrew Levin, a Dartmouth College economist who spent 20 years at the Fed.

A New York Fed spokesman declined to comment. But in a statement this month, the leaders of the bank’s search committee said they had solicited comment from a variety of groups and had interviewed a range of candidates.

In recent years, progressive groups have put increasing pressure on the Fed to diversify its leadership and to become more responsive to public concerns about inequality, slow wage growth and other issues that are outside its traditional mandate of ensuring maximum employment and stable prices. The effort has scored some notable victories, including the appointment last year of Raphael W. Bostic in Atlanta as the first African-American president of a regional Fed bank.

Mr. Dudley’s announcement last fall that he would step down represented the movement’s greatest opportunity yet. The president of the New York Fed, unique among the heads of the 12 regional banks, has a permanent vote on the F.O.M.C. and serves as the committee’s vice chairman. The New York bank also plays a crucial role in carrying out the Fed’s policies, and in overseeing many of the country’s largest financial institutions.

Those pushing for change had reason to hope their voices would be heard. In the past, the selection of Fed presidents has been heavily influenced by the financial institutions that are formally the stockholders of the Fed’s regional banks. But the regulatory overhaul after the financial crisis removed the banks’ representatives from the selection process. One of the two leaders of the search for Mr. Dudley’s successor is Sara Horowitz, who runs the Freelancers Union, a labor organization. The other, Glenn Hutchins, is a private equity investor.

In early March, several dozen protesters marched to the New York Fed’s headquarters in Lower Manhattan to demand an appointee representing workers’ interests. Standing outside the Fed’s imposing stone building on Maiden Lane, Shawn Sebastian, director of the Fed Up campaign, which seeks to make the central bank more responsive to labor concerns, said the board could “make history” by appointing someone without Wall Street ties.