We present the relation between the star formation rate density, Ssfr, and the hydrostatic mid-plane pressure, Phyd, for 4260 star-forming regions of kpc size located in 96 galaxies included in the EDGE-CALIFA survey. We find that these two parameters are tightly correlated, exhibiting a smaller scatter and a stronger correlation in comparison to other star-forming scaling relation. A power-law, with a slightly sub-linear exponent, is a good representation of this relation. Our analysis suggests that the primary channel of self regulation of the Ssfr at kpc scales comes from momentum flux injection to the interstellar medium from supernovae explosions. However, other channels of pressure in disk galaxies may also play a significant role in shaping the Ssfr at local scales. Our results also suggest that Phyd can be consider as the main driver of the star formation at kpc scales, rather than individual components of the baryonic mass.