Plants under water deficit reduce leaf growth, thereby reducing transpiration rate at the expense of reduced photosynthesis. The objective of this work was to analyse the response of leaf growth to water deficit in several sunflower genotypes in order to identify and quantitatively describe sources of genetic variability for this trait that could be used to develop crop varieties adapted to specific scenarios. The genetic variability of the response of leaf growth to water deficit was assessed among 18 sunflower (Helianthus annuus L.) inbred lines representing a broad range of genetic diversity. Plants were subjected to long-term, constant-level, water-deficit treatments, and the response to water deficit quantified by means of growth models at cell-, leaf-, and plant-scale. Significant variation among lines was found for the response of leaf expansion rate and of leaf growth duration, with an equal contribution of these responses to the variability in the reduction of leaf area. Increased leaf growth duration under water deficit is usually suggested to be caused by changes in the activity of cell-wall enzymes, but the present results suggest that the duration of epidermal cell division plays a key role in this response. Intrinsic genotypic responses of rate and duration at a cellular scale were linked to genotypic differences in whole-plant leaf area profile to water deficit. The results suggest that rate and duration responses are the result of different physiological mechanisms, and therefore capable of being combined to increase the variability in leaf area response to water deficit.