Mayor Bill de Blasio's administration is seeking $40 million in state funding to launch a new rental subsidy program to combat an unprecedented level of homelessness in New York City, part of a multifaceted policy proposal that officials plan to outline Monday.

Gilbert Taylor, commissioner of the city's Department of Homeless Services, is scheduled to provide the most detailed accounting of the administration's plans to reduce homelessness when he testifies before the City Council at a budget oversight hearing Monday. As of...