The formation of the first monolayer of water molecules on bare dust grains is of primary importance to understand the growth of the icy mantles that cover dust in the interstellar medium. In this work, we explore experimentally the formation of water molecules from O(2) + D reaction on bare silicate surfaces that simulates the grains present in the diffuse interstellar clouds at visual extinctions (A(V) < 3 mag). For comparison, we also study the formation of water molecules on surfaces covered with amorphous water ice representing the dense clouds (A(V) ≥ 3 mag). Our studies focus on the formation of water molecules in the sub-monolayer and monolayer regimes using reflection absorption infrared spectroscopy and temperature-programmed desorption techniques. We provide the fractions of the products, such as D(2)O and D(2)O(2) molecules formed on three astrophysically relevant surfaces held at 10 K (amorphous olivine-type silicate, porous amorphous water ice, and nonporous amorphous water ice). Our results showed that the formation of D(2)O molecules occurs with an efficiency of about 55%-60% on nonporous amorphous water ice and about 18% on bare silicate grains surfaces. We explain the low efficiency of D(2)O water formation on the silicate surfaces by the desorption upon formation of certain products once the reaction occurs between O(2) and D atoms on the surface. A kinetic model taking into account the chemical desorption of newly formed water supports our conclusions.