Abstract: Thermal dark matter models with particle chi masses below the electroweak scale can provide an explanation for the observed relic dark matter density. This would imply the existence of a new feeble interaction between the dark and ordinary matter. We report on a new search for the sub-GeV chi production through the interaction mediated by a new vector boson, called the dark photon A ' , in collisions of 100 GeV electrons with the active target of the NA64 experiment at the CERN SPS. With 9.37 x 10(11) electrons on target collected during 2016-2022 runs NA64 probes for the first time the well-motivated region of parameter space of benchmark thermal scalar and fermionic dark matter models. No evidence for dark matter production has been found. This allows us to set the most sensitive limits on the A ' couplings to photons for masses m(A ') less than or similar to 0.35 GeV, and to exclude scalar and Majorana dark matter with the chi – A ' coupling alpha(D) <= 0.1 for masses 0.001 less than or similar to m(chi) less than or similar to 0.1 GeV and 3m(chi) <= m(A ').