We present a neurocomputational controller for robotic manipulation based on the recently developed “neural virtual machine” (NVM). The NVM is a purely neural recurrent architecture that emulates a Turing-complete, purely symbolic virtual machine. We program the NVM with a symbolic algorithm that solves blocks-world restacking problems, and execute it in a robotic simulation environment. Our results show that the NVM-based controller can faithfully replicate the execution traces and performance levels of a traditional non-neural program executing the same restacking procedure. Moreover, after programming the NVM, the neurocomputational encodings of symbolic block stacking knowledge can be fine-tuned to further improve performance, by applying reinforcement learning to the underlying neural architecture.