In this research, we study the effects of a single giant planet on the dynamical evolution of water-rich embryos and planetesimals, located beyond the snow line of systems around Sun-like stars, in order to determine what kind of terrestrial-like planets could be formed in the habitable zone (HZ) of these systems. To do this, we carry out N-body simulations of planetary accretion, considering that the gas has been already dissipated from the disc and a single giant planet has been formed beyond the snow line of the system, at 3 au. We find that a giant planet with a value of mass between Saturn mass and Jupiter mass represents a limit from which the amount of water-rich embryos that move inward from beyond the snow line starts to decrease. From this, our research suggests that giant planets more massive than one Jupiter mass become efficient dynamical barriers to inward-migrating water-rich embryos. Moreover, we infer that the number of these embryos that survive in the HZ decreases significantly for systems that host a giant planet more massive than one Jupiter mass. This result has important consequences concerning the formation of terrestrial-like planets in the HZ with very high water content and could provide a selection criterion in the search for potentially habitable exoplanets in systems that host a gaseous giant around solar-type stars.Instituto de Astrofísica de La Plata