WASHINGTON — The Supreme Court on Tuesday will try to balance the rights of Americans who have not been convicted of a major crime to keep their DNA out of the government’s hands against the rights of crime victims to see justice done.

If the court rules for Alonzo King of Maryland, more than 1 million DNA profiles that have been stored in a federal database for matching with future crime scene evidence may have to be purged, advocates say. Others will never be collected, leading some repeat offenders to go free.