Differential inclusive jet cross sections in neutral current deep inelastic ep scattering have been measured with the ZEUS detector using an integrated luminosity of 38.7 pb-1. The jets have been identified using the kT cluster algorithm in the longitudinally invariant inclusive mode in the laboratory frame; they have been selected with jet transverse energy, ETjet above 6 GeV and jet pseudorapidity, ηjet, between -1 and 3. Measurements of cross sections as functions of ETjet, Björken x and the photon virtuality, Q2, are presented. Three phase-space regions have been selected in order to study parton dynamics from the most global to the most restrictive region of forward-going (close to the proton-beam direction) jets at low x, where the effects of BFKL evolution might be present. The measurements have been compared to the predictions of leading-logarithm parton-shower Monte Carlo models and fixed-order perturbative QCD calculations. In the forward region, O (αs1) QCD calculations underestimate the data up to an order of magnitude at low x. An improved description of the data in this region is obtained by including O (αs2) QCD corrections, which account for the lowest-order t̂-channel gluon-exchange diagrams, highlighting the importance of such terms in the parton dynamics at low x. © 2005 Elsevier B.V. All rights reserved.