Mayor Michael Bloomberg on Tuesday blamed the state and advocates for the poor for a disturbing rise in people sleeping at New York City homeless shelters, saying Albany killed a rent subsidy that helped pay for permanent homes.

The funding likely won't be restored soon. The Bloomberg administration isn't lobbying Gov. Andrew Cuomo or state lawmakers for the money, according to people familiar with the matter. Advocates said Mr. Bloomberg is leaving to the next mayor the task of controlling a shelter population that has grown...