Transrectal biopsies under 2D ultrasound (US) control are the current clinical standard for prostate cancer diagnosis. The isoechogenic nature of prostate carcinoma makes it necessary to sample the gland systematically, resulting in a low sensitivity. Also, it is difficult for the clinician to follow the sampling protocol accurately under 2D US control and the exact anatomical location of the biopsy cores is unknown after the intervention. Tracking systems for prostate biopsies make it possible to generate biopsy distribution maps for intra- and post-interventional quality control and 3D visualisation of histological results for diagnosis and treatment planning. They can also guide the clinician toward non-ultrasound targets. In this paper, a volume-swept 3D US based tracking system for fast and accurate estimation of prostate tissue motion is proposed. The entirely image-based system solves the patient motion problem with an a priori model of rectal probe kinematics. Prostate deformations are estimated with elastic registration to maximize accuracy. The system is robust with only 17 registration failures out of 786 (2%) biopsy volumes acquired from 47 patients during biopsy sessions. Accuracy was evaluated to 0.76±0.52mm using manually segmented fiducials on 687 registered volumes stemming from 40 patients. A clinical protocol for assisted biopsy acquisition was designed and implemented as a biopsy assistance system, which allows to overcome the draw-backs of the standard biopsy procedure.