WASHINGTON — A proposed federal bill of rights for survivors of sexual assault won final legislative approval Wednesday, sending it to the president’s desk.

The measure, approved by voice vote in the Senate, would ensure that survivors in federal criminal cases have the right to a sexual assault evidence collection kit, to be told of the results and to be notified in writing before the kit is destroyed.

Lawmakers say they are troubled by the number of untested rape kits that remain in the country, despite efforts to reduce a national backlog.

The bill was prompted by Amanda Nguyen, a former Harvard University student who was sexually assaulted in Massachusetts and now leads an advocacy group that helps assault survivors.

Nguyen told lawmakers that the trauma of her assault was made worse by her experience with a criminal justice system she came to believe was working against her, not for her. Nguyen was repeatedly required to return to Massachusetts to prevent destruction of her rape kit, for instance, and struggled to keep up with developments in the legal case.

Sen. Jeanne Shaheen, D-N.H., said Nguyen and other sexual assault survivors “face heartbreaking challenges” as they navigate a maze of policies and laws that differ from state to state, and even among jurisdictions.

“Survivors of sexual assault like Amanda need to know the government and justice system are on their side,” Shaheen said, calling the voice vote in favor of the bill “a strong signal to survivors across the country” that Congress is are committed to changing the culture around how sexual assault survivors will be treated in the criminal justice system.

“Sexual assault remains one of the most underreported crimes and I sincerely hope that these basic rights make it easier for survivors to come forward and pursue justice,” Shaheen said.

Sen. Chuck Grassley, R-Iowa, chairman of the Senate Judiciary Committee, also hailed the bill.

“Each and every survivor of sexual assault should have equal access to all available tools in their pursuit of justice. This includes proper collection and preservation of forensic evidence,” Grassley said.

He and other supporters said the bill should serve as a model for states to ensure that survivors receive fair and consistent treatment.