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Abstract A clear definition of the contribution from the slow neutron-capture process (s process) to the solar abundances between Fe and the Sr-Zr region is a crucial challenge for nuclear astrophysics. Robust s-process predictions are necessary to disentangle the contribution from other stellar processes producing elements in the same mass region. Nuclear uncertainties are affecting s-process calculations, but most of the needed nuclear input are accessible to present nuclear experiments or they will be in the near future. Neutron-capture rates have a great impact on the s process in massive stars, which is a fundamental source for the solar abundances of the lighter s-process elements heavier than Fe (weak s-process component). In this work we present a new nuclear sensitivity study to explore the impact on the s process in massive stars of 86 neutron-capture rates, including all the reactions between C and Si and between Fe and Zr. We derive the impact of the rates at the end of the He-burning core and at the end of the C-burning shell, where the$$^{22}$$ ${}^{22}$Ne($$\alpha $$ $\alpha$,n)$$^{25}$$ ${}^{25}$Mg reaction is is the main neutron source. We confirm the relevance of the light isotopes capturing neutrons in competition with the Fe seeds as a crucial feature of the s process in massive stars. For heavy isotopes we study the propagation of the neutron-capture uncertainties, finding a clear difference of the impact of Fe and Co isotope rates with respect to the rates of heavier stable isotopes. The local uncertainty propagation due to the neutron-capture rates at the s-process branching points is also considered, discussing the example of$$^{85}$$ ${}^{85}$Kr. The complete results of our study for all the 86 neutron-capture rates are available online. Finally, we present the impact on the weak s process of the neutron-capture rates included in the new ASTRAL library (v0.2).