The routine application of remote surveying techniques which can quickly acquire 3D digital data with high resolution, in particular digital photogrammetry, light detection and ranging (LiDAR) and unmanned aerial vehicle (UAV) for rock mass characterization has rapidly grown over the past decade. In this paper, a new method for automatic identification and interpretation of rock mass discontinuities, clustering of discontinuity sets and characterization of discontinuity orientation, persistence and spacing using 3D point clouds, is presented. The proposed method is based on a four-stage procedure consisting of: (1) normal vector calculation using the iterative reweighted plane fitting (IRPF) method, (2) discontinuity sets clustering by fast search and find of density peaks (CFSFDP) algorithm, and Fisher’s K value iterative calculation to eliminate noise points, (3) discontinuity segmentation using density-ratio based method, and discontinuity plane fitting using the random sample consensus (RANSAC) algorithm, (4) persistence and spacing calculation using the theory of analytic geometry. The method is applied to two case studies (i.e. rock slopes) and compared with the results from previous studies and from manual survey. It is concluded that the proposed method is reliable and yields a great accuracy for automatic identification of discontinuities in rock masses. •An automatic method using machine learning algorithms for discontinuity identification and extraction is proposed.•Several discontinuity parameters, namely number of sets, orientation, spacing and trace length can be obtained.•Discontinuity location, best fitting plane, and 3D trace mapping can also be performed.•This method is applied for two real cases and produces reliable and accuracy results.