Simulations are used to investigate for the first time the anisotropy of the dielectric response and the effects of an applied electric field E ex on the phase diagram of water. In the presence of electric fields ice II disappears from the phase diagram. When Eex is applied in the direction perpendicular to the ac crystallographic plane the melting temperatures of ices III and V increase whereas that of ice Ih is hardly affected. Ice III also disappears as a stable phase when Eex is applied in the direction perpendicular to the ab plane. Eex increases by a small amount the critical temperature and reduces slightly the temperature of the maximum density of liquid water. The presence Eex modifies all phase transitions of water but its effect on solid-solid and solid-fluid transitions seems to be more important and different depending on the direction of Eex.