The elemental abundances of symbiotic giants are essential to address the role of chemical composition in the evolution of symbiotic binaries, to map their parent population, and to trace their mass transfer history. However, the number of symbiotic giants with fairly well determined photospheric composition is still insufficient for statistical analyses. This is the third in a series of papers on the chemical composition of symbiotic giants determined from high-resolution ( R ~ 50 000), near-infrared spectra. Here we present results for 24 S-type systems. Spectrum synthesis methods employing standard local thermal equilibrium analysis and atmosphere models were used to obtain photospheric abundances of CNO and elements around the iron peak (Fe, Ti, Ni, and Sc). Our analysis reveals metallicities distributed in a wide range from slightly supersolar ([Fe/H] ~ +0.35 dex) to significantly subsolar ([Fe/H] ~ –0.8 dex) but principally with near-solar and slightly subsolar metallicity ([Fe/H] ~ –0.4 to –0.3 dex). The enrichment in 14 N isotope, found in all these objects, indicates that the giants have experienced the first dredge-up. This was confirmed in a number of objects by the low 12 C/ 13 C ratio (5–23). We found that the relative abundance of [Ti/Fe] is generally large in red symbiotic systems.