Dexterous arm reaching movements are a critical feature that allow human interactions with tools, the environment, and socially with others. Thus the development of a neural architecture providing unified mechanisms for actual, mental, observed and imitated actions could enhance robot performance, enhance human-robot social interactions, and inform specific human brain processes. Here we present a model, including a fronto-parietal network that implements sensorimotor transformations (inverse kinematics, workspace visuo-spatial rotations), for self-intended and imitation performance. Our findings revealed that this neural model can perform accurate and robust 3D actual/mental arm reaching while reproducing human-like kinematics. Also, using visuo-spatial remapping, the neural model can imitate arm reaching independently of a demonstrator-imitator viewpoint. This work is a first step towards providing the basis of a future neural architecture for combining cognitive and sensorimotor processing levels that will allow for multi-level mental simulation when executing actual, mental, observed, and imitated actions for dexterous arm movements.