Abstract We present an updated version of the mass–metallicity (MZ) relation using integral field spectroscopy data obtained from 734 galaxies observed by the CALIFA survey. These unparalleled spatially resolved spectroscopic data allow us to determine the metallicity at the same physical scale (Re) for different calibrators. We obtain MZ relations with similar shapes for all calibrators, once the scalefactors among them are taken into account. We do not find any significant secondary relation of the MZ relation with either the star formation rate (SFR) or the specific SFR for any of the calibrators used in this study, based on the analysis of the residuals of the best-fitted relation. However, we do see a hint for an (s)SFR-dependent deviation of the MZ relation at low masses (M < 109.5 M⊙), where our sample is not complete. We are thus unable to confirm the results by Mannucci et al. (2010), although we cannot exclude that this result is due to the differences in the analysed data sets. In contrast, our results are inconsistent with the results by Lara-López et al. (2010), and we can exclude the presence of an SFR–mass–oxygen abundance fundamental plane. These results agree with previous findings suggesting that either (1) the secondary relation with the SFR could be induced by an aperture effect in single fibre/aperture spectroscopic surveys, (2) it could be related to a local effect confined to the central regions of galaxies or (3) it is just restricted to the low-mass regime, or a combination of the three effects.