The differential cross section for the process Z/gamma* -> ll (l = e, mu) as a function of dilepton invariant mass is measured in pp collisions at root s = 7 TeV at the LHC using the ATLAS detector. The measurement is performed in the e and mu channels for invariant masses between 26 GeV and 66 GeV using an integrated luminosity of 1.6 fb(-1) collected in 2011 and these measurements are combined. The analysis is extended to invariant masses as low as 12 GeV in the muon channel using 35 pb(-1) of data collected in 2010. The cross sections are determined within fiducial acceptance regions and corrections to extrapolate the measurements to the full kinematic range are provided. Next-to-next-to-leading-order QCD predictions provide a significantly better description of the results than next-to-leading-order QCD calculations, unless the latter are matched to a parton shower calculation.