In 2000, New York had 17,000 untested rape kits, a yearslong accumulation of potential evidence in some of the city’s most violent crimes. Over the next four years, in a push to clear the backlog, the city had the kits tested. The result was 49 indictments connected to unsolved cases in Manhattan alone.

Seeing these efforts as a model for jurisdictions around the country to replicate, Cyrus R. Vance Jr., the Manhattan district attorney, announced a program on Wednesday under which $35 million in civil forfeiture assets will be used to help other cities and states tackle their own backlogs, which, nationally, total in the hundreds of thousands.

In an interview, Mr. Vance said the effort was likely to have an impact far beyond the communities that receive the aid.

“Rape kits that are untested are not just going to solve crimes in the jurisdictions where they are, but because some of these people are serial offenders, this could lead to solutions of crimes all over the country,” he said.

A rape kit is the collection of physical evidence gathered when a sexual assault victim is examined. Such kits are tested for DNA evidence that may identify, or rule out, suspects.

The initiative announced by Mr. Vance is intended to assist cities like Memphis, which has a backlog of 11,000 untested rape kits, and Las Vegas, which estimates its backlog at 4,000.

The program is to be run with the assistance of the Joyful Heart Foundation, a victims’ advocacy organization that for the last several years has made clearing rape-kit backlogs a priority.