Crystallization kinetics of water on Ru(0001) with and without adspecies was investigated using reflection high energy electron diffraction (RHEED). Amorphous solid water is formed on the bare Ru(0001) substrate during water vapor deposition at 135 K; randomly oriented ice Ic crystallites grow after some incubation time. The nucleation and epitaxial growth tend to be aborted on the oxygenated Ru(0001) substrate, whereas ice Ih crystallites having considerable stacking disorders grow epitaxially on the CO-adsorbed Ru(0001) substrate immediately after water deposition at 135 K. Results indicate that epitaxy is controlled by the interfacial ice nucleation time and the water deposition rate.