Context. Physical and phenomenological properties (radius, luminosity, shape of the light curve, etc.) of Cepheids strongly depend on the pulsation period, with the exception of the pulsation amplitude. A possible factor causing a wide range of pulsation amplitudes might be the different atmospheric metallicities of individual Cepheids. Aims: We studied the influence exerted by the atmospheric iron content, [Fe/H], on the pulsational amplitude of Galactic Cepheids. Methods: We searched for correlations between the [Fe/H] value and both the observed amplitudes and amplitude related parameters. Results: The amplitude of the Cepheid pulsation slightly decreases with increasing iron abundance. This effect is more pronounced for the radial velocity variations and for the shorter pulsation periods. The wavelength dependence of photometric amplitudes is also found to be sensitive to the metallicity. Some of these effects are not consequences of differential line blanketing. Based on the calibrations of the metallicity sensitivity relationships, we derived photometric iron abundance for 21 Galactic Cepheids. The dichotomic behaviour dividing Galactic Cepheids that pulsate in the fundamental mode into short- and long-period groups at the period of 10d.7 can be noticed in some diagrams that show metallicity-related dependences. Conclusions: We confirm that variety in atmospheric metallicity in Cepheids contributes to the finite range of pulsation amplitudes at a given period. Effects of metallicity on the amplitudes revealed from observational data and the occurrence of the dichotomy also derived from phenomenological data have to be confirmed by appropriate theoretical models of stellar structure and pulsation.