Evidence from up to 70,000 rape cases nationwide will get long-awaited DNA testing, the Manhattan District Attorney Cyrus R. Vance Jr. announced Wednesday as he pledged as much as $35 million to help eliminate a backlog that has long troubled authorities, victims and lawmakers.

Experts estimate hundreds of thousands of rape kits — swabs and specimens gathered during exams victims undergo after attacks — remain to be tested for genetic evidence that could identify, or eliminate, a suspect. The $500-to-$1,000-per-kit cost of testing has been major factor, despite millions in federal funding.

"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.

He announced the plan at a news conference with "Law & Order: Special Victims Unit" star and sexual assault survivors' advocate Mariska Hargitay. The money comes from the DA's share of an $8.8 billion settlement with French bank BNP Paribas over allegations of violating U.S. economic sanctions by processing transactions for clients in blacklisted countries.

New York state communities will get priority in applying for the funding. The initiative is meant to complement some $41 million President Barack Obama has proposed to devote to testing rape kits; Congress is weighing it. An existing federal law also finances such testing.

Besides testing rape kits, the money also will go to auditing how big backlogs are and making sure authorities follow the best methods for testing and using the evidence.

New York City tackled a 17,000-case backlog between 2000 and 2003. The Manhattan DA's office — one of five in the city — used the test results to bring nearly 50 indictments. Those convicted are serving sentences that add up to hundreds of years.

Other jurisdictions have been grappling with big backlogs. More than 12,000 kits went untested for years in Memphis, Tennessee, which is now working on them and facing a lawsuit from rape victims. In Detroit, prosecutors discovered more than 11,000 rape kits languishing in an abandoned police warehouse in 2009; testing there so far has yielded 14 convictions.

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Reach Jennifer Peltz on Twitter @jennpeltz.