ABSTRACT The processes that regulate star formation are essential to understand how galaxies evolve. We present the relation between star formation rate density, ΣSFR , and hydrostatic mid-plane pressure,Ph, for 4260 star-forming regions of kpc size located in 96 galaxies included in the EDGE-CALIFA survey covering a wide range of stellar masses and morphologies. We find that these two parameters are tightly correlated, showing a smaller scatter in comparison to other star-forming relations. A power law, with a slightly sublinear index, is a good representation of this relation. Its residuals show a significant anticorrelation with both stellar age and metallicity whereas the total stellar mass may also play a secondary role in shaping the ΣSFR–Ph relation. For actively star-forming regions, we find that the effective feedback momentum per unit stellar mass (p*/m*), measured from thePh/ΣSFR  ratio increases withPh. The median value of this ratio for all the sampled regions is larger than the expected momentum just from supernovae explosions. Morphology of the galaxies, including bars, does not seem to have a significant impact in the ΣSFR–Ph relation. Our analysis indicates that local ΣSFR self-regulation comes mainly from momentum injection to the interstellar medium from supernovae explosions. However, other mechanisms in disc galaxies may also play a significant role in shaping the ΣSFR at kpc scales. Our results also suggest thatPh is the main parameter that modulates star formation at kpc scales, rather than individual components of the baryonic mass.