We present a new method for estimating ice mass loss from glaciers and ice sheets using Interferometric Synthetic Aperture Radar (InSAR) time-series data. We use a linear inversion method based on observations of nearby bedrock uplift and a solution for surface loading of an elastic half-space. The method assumes that mass loss is focused on lower elevation terminal regions of the glacier or ice sheet, and that there is an exponential decrease in thinning rate toward the higher elevation interior. We apply the method to uplift rates between 1995 and 2009 near Vatnajökull, Iceland. The data reveal up to 13 mm/yr relative line-of-sight (LOS) velocity around the south-western edge of Vatnajökull. We find an ice mass loss rate of Gt/yr, in approximate agreement with other estimates. Ice loss since 1995 is twice as fast as the loss rate estimated for the rest of the 20th century.