In this paper we retrieve atmospheric HDO, H2O concentrations and their ratio δD from IASI radiances spectra. Our method relies on an existing radiative transfer model (Atmosphit) and an optimal estimation inversion scheme, but goes further than our previous work by explicitly considering correlations between the two species. A global HDO and H2O a priori profile together with a covariance matrix were built from daily LMDz-iso model simulations of HDO and H2O profiles over the whole globe and a whole year. The retrieval parameters are described and characterized in terms of errors. We show that IASI is mostly sensitive to δD in the middle troposphere and allows retrieving δD for an integrated 3-6 km column with an error of 38‰ on an individual measurement basis. We examine the performance of the retrieval to capture the temporal (seasonal and short-term) and spatial variations of δD for one year of measurement at two dedicated sites (Darwin and Izaña) and a latitudinal band from -60° to 60° for a 15 day period in January. We report a generally good agreement between IASI and the model and indicate the capabilities of IASI to reproduce the large scale variations of δD (seasonal cycle and latitudinal gradient) with good accuracy. In particular, we show that there is no systematic significant bias in the retrieved δD values in comparison with the model, and that the retrieved variability is similar to the one in the model even though there are certain local differences. Moreover, the noticeable differences between IASI and the model are briefly examined and suggest modeling issues instead of retrieval effects. Finally, the results further reveal the unprecedented capabilities of IASI to capture short-term variations in δD, highlighting the added value of the sounder for monitoring hydrological processes.