New York City will share $35m with towns across the US to help reduce the backlog of untested rape kits, Manhattan district attorney Cyrus Vance announced on Wednesday

Vance said up to 70,000 kits could be tested with the new funds. These kits contain swabs and specimens collected during victim examinations and contain information that could be used to identify and rule out suspects.

“Rape victims nationwide deserve to know that the invasive examination they underwent had a purpose, and the resulting kit was not left to gather dust on a forgotten shelf,” Vance said.

Testing a rape kit costs between $500 and $1,000 per kit. Nationwide, thousands of rape kits dating back decades have languished untested. More than 12,000 kits went untested for years in Memphis, Tennessee, where 200 more dating back as far as 1976 were recently discovered in a warehouse. In Detroit, prosecutors discovered more than 11,000 rape kits in an abandoned police warehouse in 2009; testing there so far has yielded 14 convictions.

Cleveland prosecutors have sent their entire 4,700-kit backlog for testing, so far yielding over 200 indictments and 50 convictions.

A decade ago, New York City tackled a 17,000-case backlog, resulting in more than 200 prosecutions citywide, Vance said.

The money comes from the Manhattan district attorney’s share of a $8.8bn settlement with BNP Paribas will be used to pay for the testing. The French bank agreed this summer to plead guilty to having violated US economic sanctions by hiding billions in transfers with clients in Cuba, Sudan and Iran. The deal left New York’s financial services department with about a quarter of the settlement, $2.2bn.

Vance said that the state is interested in distributing the money nationwide as a crime prevention measure.

“Rape is not a local crime,” Vance said. “Many who rape, do it again elsewhere and DNA evidence helps states and cities solve crimes across the country.”

He was joined on stage by actor Mariska Hargitay, who advocates for sexual assault survivors, and Michigan prosecutor Kym Worthy, a leader in the campaign to reduce the rape kit testing backlog.

“My fervent hope is that jurisdictions across this country that have untested rape kits will step out of the shadows,” said Worthy in a statement. She represents Wayne County, home to Detroit, where more than 11,000 untested rape kits were discovered in 2009.

Part of the money will also be used to audit the length of backlogs and ensure authorities are effectively using the kits.

The Obama administration is waiting for Congress to approve a request for $41m to reduce the backlog.

The Associated Press contributed to this report.