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Weeks after New York City officials were caught off-guard by a freakish November snowstorm, Mayor Bill de Blasio seemed to be caught flat-footed again — this time, by a botched plan to push out his emergency management commissioner, Joseph Esposito.

Firing top officials has not been the mayor’s strong suit. He rarely does it, even amid scandal. But the handling of Mr. Esposito’s departure — a three-day misadventure where no one seemed to know whether he had been fired — left even supporters of the mayor publicly challenging the process.

By the end of the night on Monday, Mr. de Blasio answered one question: Mr. Esposito would no longer be in charge of emergency management. But many questions remained — including when Mr. Esposito would actually be gone.

“We have started the process of leadership change at New York City Emergency Management,” the mayor said in a statement sent after 10 p.m. on Monday. “Commissioner Joe Esposito will continue to lead O.E.M. as we conduct a national search for his successor.”