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Context. The stellar origin of the elements molybdenum (Mo, Z = 42) and ruthenium (Ru, Z = 44) is still a matter of debate. Studying their abundances provides valuable insights into nucleosynthesis processes and the broader evolution of neutron-capture elements. Aims. The aim of this work is to present new observations of Mo and Ru, together with nearby neutron-capture elements strontium (Sr) and zirconium (Zr) for a new sample of 154 giant stars, located in the Galactic disk with metallicities −1 < [Fe/H] < +0.3. Methods. The abundances were determined under the assumption of the local thermodynamic equilibrium by fitting synthetic spectra. The abundances of Mo were derived from the Mo I lines at 5506 and 5533 Å, while the abundances of Ru were determined from Ru I lines at 4584, and 4757 Å. The abundances of Sr and Zr were measured using lines of Sr II at 4077 and 4215 Å and lines of Zr I at 5385, 6127, and 6134 Å. Results. We derived Sr, Zr, and Mo abundances for all stars in our sample, and Ru for 110 stars. For most of the giant stars observed in this work, Mo and Ru abundances were determined for the first time. We compare our observations with the signatures from different nucleosynthesis processes. Conclusions. Both the [Mo/Fe] and [Ru/Fe] in our stars show a decreasing trend with respect to increasing [Fe/H]. This pattern is similar to that of [Zr/Fe], whereas [Sr/Fe] exhibits a relatively flat trend with metallicity. These results are compatible with our previous measurements obtained for dwarf stars over the same metallicity range. Compared to the s -process ratios, all stars show a lower [Zr/Mo] and a higher [Ru/Mo], as expected from classical nucleosynthesis. Still, it is unclear if additional contributions from neutrino-wind components or the i -process is needed to explain the observed scatter of [Zr/Mo] and [Ru/Mo] in the Milky Way disk. Indeed, such a dispersion is consistent with the variations also seen in r-II stars at low metallicity and could therefore result from the combined contributions of r -process and s -process to galactic chemical evolution. The observed [Zr/Mo] and [Ru/Mo] scatter in r-II stars should be constrained by future investigations to define if any contributions of additional nucleosynthesis components are needed.