Context. The iron Kα line at 6.4 keV provides a valuable spectral diagnostic in several fields of X-ray astronomy. The line often results from the reprocessing of external hard X-rays by a neutral or low-ionized medium, but it can also be excited by impacts of low-energy cosmic rays. Aims: This paper aims to provide signatures allowing identification of radiation from low-energy cosmic rays in X-ray spectra showing the 6.4 keV Fe Kα line. Methods: We study in detail the production of nonthermal line and continuum X-rays by interaction of accelerated electrons and ions with a neutral ambient gas. Corresponding models are then applied to XMM-Newton observations of the X-ray emission emanating from the Arches cluster region near the Galactic center. Results: Bright 6.4 keV Fe line structures are observed around the Arches cluster. This emission is very likely produced by cosmic rays. We find that it can result from the bombardment of molecular gas by energetic ions, but probably not by accelerated electrons. Using a model of X-ray production by cosmic-ray ions, we obtain a best-fit metallicity of the ambient medium of 1.7 ± 0.2 times the solar metallicity. A large flux of low-energy cosmic ray ions could be produced in the ongoing supersonic collision between the star cluster and an adjacent molecular cloud. We find that a particle acceleration efficiency in the resulting shock system of a few percent would give enough power in the cosmic rays to explain the luminosity of the nonthermal X-ray emission. Depending on the unknown shape of the kinetic energy distribution of the fast ions above ~1 GeV nucleon-1, the Arches cluster region may be a source of high-energy γ-rays detectable with the Fermi Gamma-ray Space Telescope. Conclusions: At present, the X-ray emission prominent in the 6.4 keV Fe line emanating from the Arches cluster region probably offers the best available signature for a source of low-energy hadronic cosmic rays in the Galaxy. Appendices are available in electronic form at http://www.aanda.org