Several techniques have been developed in the past to handle the inverse kinematics of serial robots passing through or close to singular configurations. As a common line, these approaches operate at velocity level, seeking a trade-off between tracking accuracy and joint velocity feasibility. While providing robust control, some difficulties arise in these methods for predicting end-effector errors and their spread in SE(3). In a previous paper, the virtual redundant axis (VRA) method was introduced at velocity level, by which end-effector velocity errors could be concentrated in non-controllable directions. The present paper extends the VRA method to position level, allowing for a precise motion tracking and the handling of singularity paths in the same way as regular motions.