This paper describes a highly efficient method for lossless compression of volumetric sets of medical images, such as CTs or MRIs. The proposed method, referred to as 3D-MRP, is based on the principle of minimum rate predictors (MRP), which is one of the state-of-the-art lossless compression technologies, presented in the data compression literature. The main features of the proposed method include the use of 3D predictors, 3D-block octree partitioning and classification, volume-based optimisation and support for 16 bit-depth images. Experimental results demonstrate the efficiency of the 3D-MRP algorithm for the compression of volumetric sets of medical images, achieving gains above 15% and 12% for 8 bit and 16 bit-depth contents, respectively, when compared to JPEG-LS, JPEG2000, CALIC, HEVC, as well as other proposals based on MRP algorithm.