I've never had a kiev, but I had a similar problem with my fed. The screw holding the take-up spool needed to be loosened a little. The rewind bitton only disengages the sprockets, not the take-up spool, so the take up spool needs to slip backwards to allow you to rewind the film. Once you get the tension adjusted so that there is just enough to wind the film snug from the sprockets to the take-up spool, rewinding should be OK. I can turn the take-up spool with my fingers (slipping) and everything works fine.
Rick.