This paper deals with the generalized regularization proximal point method which was introduced by the authors in [Four parameter proximal point algorithms, Nonlinear Anal. 74 (2011), 544-555]. It is shown that sequences generated by it converge strongly under minimal assumptions on the control parameters involved. Thus the main result of this paper unifies several results related to the prox-Tikhonov method, the contraction proximal point algorithm and/or the regularization method as well as some results of the above quoted paper.