The classic regelation experiment of Thomson in the 1850s deals with cutting an ice cube, followed by refreezing. The cutting was attributed to pressure-induced melting but has been challenged continuously, and only lately consensus emerged by understanding that compression shortens the O:H nonbond and lengthens the H–O bond simultaneously. This H–O elongation leads to energy loss and lowers the melting point. The hot debate survived well over 150 years, mainly due to a poorly defined heat exchange with the environment in the experiment. In our current experiment, we achieved thermal isolation from the environment and studied the fully reversible ice–liquid water transition for water confined between graphene and muscovite mica. We observe a transition from two-dimensional (2D) ice into a quasi-liquid phase by applying a pressure exerted by an atomic force microscopy tip. At room temperature, the critical pressure amounts to about 6 GPa. The transition is completely reversible: refreezing occurs when the applied pressure is lifted. The critical pressure to melt the 2D ice decreases with temperature, and we measured the phase coexistence line between 293 and 333 K. From a Clausius–Clapeyron analysis, we determine the latent heat of fusion of two-dimensional ice at 0.15 eV/molecule, being twice as large as that of bulk ice.