A new Gibbs thermodynamic potential function of ice Ih is proposed to extend and improve already existing ones and to unify various data and formulas for thermodynamic equilibrium properties of natural ice in a consistent manner. It is valid for absolute pressures from 0 to 211 MPa and for temperatures from 0 to 273.16 K. It is consistent with the current 1995 international scientific pure water standard, IAPWS-95, and with the latest 2003 Gibbs potential of seawater. In conjunction with the latter, it provides freezing temperatures of seawater for pressures up to 100 MPa (10,000 dbar). The potential functions of ice and seawater, if combined into a thermodynamic potential function of sea ice, provide all its thermodynamic equilibrium properties over the entire 'Neptunian' ranges of pressures and temperatures and brine practical salinities up to 42 (up to 50 at the surface). The new potential function of ice is compiled from an extended set of 26 groups with 339 experimental data points. It obeys the theoretical cubic law of Debye for low-temperature heat capacity, and pressure independence of zero-point entropy. Using the statistically derived residual entropy of Pauling, a physically well-grounded value for the entropy of liquid water at the triple point is provided. The severe 100% compressibility uncertainty of ice, present in former versions of the Gibbs potential, could be reduced to only 1% at normal pressure using various data on elastic lattice constants. The very high accuracy of the Clausius-Clapeyron coefficient at normal pressure of this formulation, which is 100 times more accurate than that of the 1994 international equation for the melting pressure, permits a precise determination of the normal melting temperature to be 273.152 518 K ± 2 μK. On the other hand, users of the new function should be cautioned that some of the background data have been obtained from specimens of uncertain purity and crystalline perfection. The potential function is expressed in the 1990 International Temperature Scale ITS-90.