Aims. The iron abundance gradient in the Galactic stellar disk provides fundamental constraints on the chemical evolution of this important Galaxy component, however the spread around the mean slope is, at fixed Galactocentric distance, more than the estimated uncertainties. Methods. To provide quantitative constraints on these trends, we adopted iron abundances for 265 classical Cepheids (more than 50% of the currently known sample) based either on high-resolution spectra or on photometric metallicity indices. Homogeneous distances were estimated using near-infrared period-luminosity relations. The sample covers the four disk quadrants, and their Galactocentric distances range from 5 to 17kpc. We provided a new theoretical calibration of the metallicity-index-color (MIC) relation based on Walraven and NIR photometric passbands. Results. We estimated the photometric metallicity of 124 Cepheids. Among them 66 Cepheids also have spectroscopic iron abundances and we found that the mean difference is dex. We also provide new iron abundances, based on high-resolution spectra, for four metal-rich Cepheids located in the inner disk. The remaining iron abundances are based on high-resolution spectra collected by our group (73) or available in the literature (130). A linear regression over the entire sample provides an iron gradient of dexkpc-1. The above slope agrees quite well, within the errors, with previous estimates based either on Cepheids or on open clusters covering similar Galactocentric distances. However, Cepheids located in the inner disk systematically appear more metal-rich than the mean metallicity gradient. Once we split the sample into inner (kpc) and outer disk Cepheids, the slope (dexkpc-1) in the former region is 3times steeper than the slope in the latter one (dexkpc-1). In the outer disk the radial distribution of metal-poor (MP, [Fe/H]<-0.02dex) and metal-rich (MR) Cepheids across the four disk quadrants does not show a clear trend when moving from the innermost to the external disk regions. The relative fractions of MP and MR Cepheids in the 1st and in the 3rd quadrants differ at the 8(MP) and 15(MR) levels. Finally, we found that iron abundances in two local overdensities of the 2nd and of the 4th quadrant cover individually a range in iron abundance of 0.5dex. Conclusions. Current findings indicate that the recent chemical enrichment across the Galactic disk shows a clumpy distribution. Key words: stars: variables: Cepheids - galaxy: disk - stars: oscillations - stars: abundances - stars: evolution- galaxy: stellar content
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