NLTE line formation calculations of Fe i in the solar atmosphere are extended to include weak lines in the visual spectrum of the Sun . Previously established atomic models are used to discriminate between different ways of treating collisional interaction processes . As indicated by the analysis of strong Fe i lines , the influence of deviations from LTE in the solar atmosphere on the Fe abundance is small for all lines . To derive a common solar Fe i abundance from both strong and weak lines fine-tuning of the microturbulence velocity parameter and the van der Waals damping constants is required . The solar Fe i abundances based on all available f -values are dominated by the large scatter already found for the stronger lines . In particular the bulk of the data from the work of May et al . and O ’ Brian et al . is not adequate for accurate abundance work . Based on f -values measured by the Hannover and Oxford groups alone , the Fe i LTE abundances are \log \varepsilon _ { { Fe \textsc { i } } , \odot } = 7.57 for the empirical and \log \varepsilon _ { { Fe \textsc { i } } , \odot } = 7.48 \ldots 7.51 for the line-blanketed solar model . The solar Fe ionization equilibrium obtained for different atomic and atmospheric models rules out NLTE atomic models with a low efficiency of hydrogen collisions . At variance with Paper I , it is now in better agreement with laboratory Fe ii f -values for all types of line-blanketed models . Our final model assumptions consistent with a single unique solar Fe abundance \log \varepsilon _ { Fe, \odot } \sim 7.48 \ldots 7.51 calculated from NLTE line formation are ( a ) a line-blanketed solar model atmosphere , ( b ) an iron model atom with hydrogen collision rates 0.5 < S _ { H } < 5 times the standard value to compensate for the large photoionization cross-sections , ( c ) a microturbulence velocity \xi _ { t } = 1.0 km s ^ { -1 } , ( d ) van der Waals damping parameters decreased by \Delta \log C _ { 6 } = -0.10 \ldots - 0.15 as compared to Anstee & O ’ Mara ’ s calculations , depending on S _ { H } , ( e ) Fe ii f -values as published by Schnabel et al. , and ( f ) Fe i f -values published by the Hannover and Oxford groups .