We report on a detailed study of the Fe K emission/absorption complex in the nearby, bright Seyfert 1 galaxy Mrk 509. The study is part of an extensive XMM-Newton monitoring consisting of 10 pointings (~60 ks each) about once every four days, and includes also a reanalysis of previous XMM-Newton and Chandra observations. Mrk 509 shows a clear (EW=58 eV) neutral Fe Kalpha emission line that can be decomposed into a narrow (sigma=0.027 keV) component (found in the Chandra HETG data) plus a resolved (sigma=0.22 keV) component. We find the first successful measurement of a linear correlation between the intensity of the resolved line component and the 3-10 keV flux variations on time-scales of years down to a few days. The Fe Kalpha reverberates the hard X-ray continuum without any measurable lag, suggesting that the region producing the resolved Fe Kalpha component is located within a few light days-week (r<~10^3 rg) from the Black Hole (BH). The lack of a redshifted wing in the line poses a lower limit of >40 rg for its distance from the BH. The Fe Kalpha could thus be emitted from the inner regions of the BLR, i.e. within the ~80 light days indicated by the Hbeta line measurements. In addition to these two neutral Fe Kalpha components, we confirm the detection of weak (EW~8-20 eV) ionised Fe K emission. This ionised line can be modeled with either a blend of two narrow FeXXV and FeXXVI emission lines or with a single relativistic line produced, in an ionised disc, down to a few rg from the BH. Finally, we observe a weakening/disappearing of the medium and high velocity high ionisation Fe K wind features found in previous XMM-Newton observations. This campaign has made possible the first reverberation measurement of the resolved component of the Fe Kalpha line, from which we can infer a location for the bulk of its emission at a distance of r~40-1000 rg from the BH.
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