The interaction of ozone with ice films under high vacuum was studied with single reflection Fourier transform infrared spectroscopy (incidence angle of 5 degrees). Both amorphous and crystalline ice were investigated. On amorphous ice which has a high density of free surface OH groups two states of stone were observed: one which forms a hydrogen bond with the ice surface of the micropores, and a second which is attributed to a physisorbed state. Only the latter state is observed on the crystalline ice surface. When chemisorbed ozone is covered by an amorphous film, a temperature increase above 60 K leads to diffusion (with a weak yield) of ozone in the water lattice. Absorbed ozone remains in the ice bulk until sublimation of the ice film near 155 K.