How to reduce points by proximity

I got a layer with over 4 million points. The distance between the points are 1 meter.

How can i reduce the data so that no points have less than e.g. 10 meters between them?

Maybe is not the fastest way but you could achieve this in three steps:

Convert your points to raster: Raster -> Conversion -> Rasterize

Reduce the resolution: Raster -> Conversion -> Translate (Outsize)

Convert your resized raster back to points again using the SAGA pluguin. Algorithm -> Grid values to points.

However, I'm still not sure about what you want to accomplish, as @Simbamangu said usually it is not a good idea just to eliminate data. Maybe you need to average, sum, interpolate…

In the top toolbar: Vector > Shape Tools > Geodesic Geometry Simplification > Geodesic point decimate. You can then specify the input layer, specify the minimum distance between points, and save the output layer in specified directory.