Context : In the framework of the study of the Galactic metallicity gradient and its time evolution , we present new high-resolution spectroscopic observations obtained with FLAMES and the fiber link to UVES at VLT of three open clusters ( OCs ) located within \sim 7 kpc from the Galactic Center ( GC ) : NGC 6192 , NGC 6404 , NGC 6583 . We also present new orbit determination for all OCs with Galactocentric distances ( R _ { GC } ) \leq 8 kpc and metallicity from high-resolution spectroscopy . Aims : We aim to investigate the slope of the inner disk metallicity gradient as traced by OCs and at discussing its implication on the chemical evolution of our Galaxy . Methods : We have derived memberships of a group of evolved stars for each clusters , obtaining a sample of 4 , 4 , and 2 member stars in NGC 6192 , NGC 6404 , and NGC 6583 , respectively . Using standard LTE analysis we derived stellar parameters and abundance ratios for the iron-peak elements Fe , Ni , Cr , and for the \alpha -elements Al , Mg , Si , Ti , Ca . We calculated the orbits of the OCs currently located within 8 kpc from the GC , and discuss their implication on the present-time radial location . Results : The average metallicities of the three clusters are all oversolar : [ Fe/H ] = +0.12 \pm 0.04 ( NGC 6192 ) , +0.11 \pm 0.04 ( NGC 6404 ) , +0.37 \pm 0.03 ( NGC 6583 ) . They are in qualitative agreement with their Galactocentric distances , being all internal OCs , and thus expected to be metal richer than the solar neighborhood . The abundance ratios of the other elements over iron [ X/Fe ] are consistent with solar values . Conclusions : The clusters we have analysed , together with other OC and Cepheid data , confirm a steep gradient in the inner disk , a signature of an evolutionary rate different than in the outer disk .