If the person is trying to blackmail you (i.e., threatening to go public if you do not do so and so) you should file a police report. Blackmail is a crime and the police are equipped to deal with the situation. If there is no blackmail involved, there is likely nothing you can do until this person does make the false accusations. You will have a defamation claim once someone makes the false accusations, but not before.
As a side note, if this is occurring in a work or school situation, I would recommend bringing the issue to an administrator who can help you. False accusations in those environments can be especially damaging and most organizations are prepared to address these types of issues. If this is in a school setting, this person's behavior likely constitutes bullying and school officials will act quickly to resolve the problem.
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