New York City Mayor Bill de Blasio is seeking a new head of the Office of Emergency Management, but Commissioner Joseph Esposito will remain on the job during the search for his successor.

The announcement caps a weekend of confusion over Mr. Esposito’s status. On Friday, Deputy Mayor Laura Anglin fired Mr. Esposito after a heated meeting over his agency’s response to a November snowstorm that crippled the city’s evening commute, according to people familiar with the matter.

Mr....