City officials have acknowledged the criticisms, while also defending how they have managed the effort. “There is no perfect process when it comes to choosing public art,” Jimmy Van Bramer of Queens, chairman of the City Council committee that oversees cultural affairs, said. “The community has to be involved at all levels, but there are going to be cases where it’s impossible to find consensus and people are going to be unsatisfied.”

Historically, memorials often came prepackaged by wealthy patrons who financed their projects and picked their artists. The city was typically asked only to advise and confirm the final location of monuments, which were not constructed on any deadlines — East Harlem’s Duke Ellington Memorial, for example, took nearly 20 years to complete.

By comparison, the de Blasio administration aims to finish many of its statues in two to three years, while trying to maintain at least an appearance of democratic decision-making.

Mitchell L. Moss, a professor of urban policy and planning at New York University, said that the struggles over the statues were a reflection of the charged politics of the day, especially among liberals who feel empowered locally and powerless nationally. It is happening beyond New York as well: this month San Francisco rescinded a commission for a large bronze portrait of the author Maya Angelou after public calls for a more traditional, figurative statue.

“They have no power in Washington,” Mr. Moss said of those speaking out, “so they’re going to find a way to express their values and if they have to do it though every statue that has to be updated or revised, so be it.”

In Washington, the city’s public art program has tried to avoid such protests by soliciting public input early and including residents on judging panels. “When you just drop something into someone’s community it’s the equivalent to someone dropping a work of art in your living room,” said Sandy Bellamy, who runs the program.