The photoproduction process of neutral kaons on a liquid deuterium target is investigated near the threshold region, Eγ=0.8-1.1 GeV. K0 events are reconstructed from positive and negative pions, and differential cross sections are derived. Experimental momentum spectra are compared with those calculated in the spectator model using a realistic deuteron wave function. Elementary amplitudes as given by recent isobar models and a simple phenomenological model are used to study the effect of the new data on the angular behavior of the elementary cross section. The data favor a backward-peaked angular distribution of the elementary n(γ,K0)Λ process, which provides additional constraints on current models of kaon photoproduction. The present study demonstrates that the n(γ,K0)Λ reaction can provide key information on the mechanism of the photoproduction of strangeness.