A search is presented for the pair production of new heavy resonances, each decaying into a top quark (t) or antiquark and a gluon (g). The analysis uses data recorded with the CMS detector from proton-proton collisions at a center-of-mass energy of 13 TeV at the LHC, corresponding to an integrated luminosity of 138 fb(-1). Events with one muon or electron, multiple jets, and missing transverse momentum are selected. After using a deep neural network to enrich the data sample with signal-like events, distributions in the scalar sum of the transverse momenta of all reconstructed objects are analyzed in the search for a signal. No significant deviations from the standardmodel prediction are found. Upper limits at 95% confidence level are set on the product of cross section and branching fraction squared for the pair production of excited top quarks in the t* -> tg decay channel. The upper limits range from 120 to 0.8 fb for a t* with spin-1/2 and from 15 to 1.0 fb for a t* with spin-3/2. These correspond to mass exclusion limits up to 1050 and 1700 GeV for spin-1/2 and spin-3/2 t* particles, respectively. These are the most stringent limits to date on the existence of t* -> tg resonances.