A measurement is reported of differential top quark pair (t¯t) production cross sections, where top quarks are produced at large transverse momenta. The data collected with the CMS detector at the LHC are from pp collisions at a center-of-mass energy of 13  TeV corresponding to an integrated luminosity of 35.9  fb−1. The measurement uses events where at least one top quark decays as t→Wb→q¯q′b and is reconstructed as a large-radius jet with transverse momentum in excess of 400 GeV. The second top quark is required to decay either in a similar way or leptonically, as inferred from a reconstructed electron or muon, a bottom quark jet, and missing transverse momentum due to the undetected neutrino. The cross section is extracted as a function of kinematic variables of individual top quarks or of the t¯t system. The results are presented at the particle level, within a region of phase space close to that of the experimental acceptance, and at the parton level and are compared to various theoretical models. In both decay channels, the observed absolute cross sections are significantly lower than the predictions from theory, while the normalized differential measurements are well described.