Inclusive-jet and dijet differential cross sections have been measured in neutral current deep inelastic ep scattering for exchanged boson virtualities Q(2) > 125 GeV2 with the ZEUS detector at HERA using an integrated luminosity of 82 pb(-1). Jets were identified in the Breit frame using the k(T) cluster algorithm. Jet cross sections are presented as functions of several kinematic and jet variables. The results are also presented in different regions of Q2. Next-to-leading-order QCD calculations describe the measurements well. Regions of phase space where the theoretical uncertainties are small have been identified. Measurements in these regions have the potential to constrain the gluon density in the proton when used as inputs to global fits of the proton parton distribution functions. (c) 2006 Published by Elsevier B.V.