Dijet production has been studied in neutral current deep inelastic e+p scattering for 470 < Q2 < 20000 GeV2 with the ZEUS detector at HERA using an integrated luminosity of 38.4 pb-1. Dijet differential cross sections are presented in a kinematic region where both theoretical and experimental uncertainties are small. Next-to-leading-order (NLO) QCD calculations describe the measured differential cross sections well. A QCD analysis of the measured dijet fraction as a function of Q2 allows both a precise determination of αs(Mz) and a test of the energy-scale dependence of the strong coupling constant. A detailed analysis provides an improved estimate of the uncertainties of the NLO QCD cross sections arising from the paxton distribution functions of the proton. The value of αs(Mz), as determined from the QCD fit, is αs (MZ) = 0.1166 ± 0.0019(stat.)+0.0024-0.0044 (exp.) +0.00570.0044(th.). © 2001 Elsevier Science B.V.