Touch-sensitive stretchable electronic skins (e-skins) hold promise for soft robots, prosthetics, bio-mimetics, and bio-sensors. However, a long-standing challenge has been the interference of stretching in pressure readings. Addressing this, we introduce an intrinsically stretchable hybrid response pressure sensor (SHRPS) composed of a laminate featuring a barely conductive porous nanocomposite and an ultrathin dielectric layer situated between two stretchable electrodes. The combined piezoresistive and piezocapacitive responses of the SHRPS enable ultrahigh pressure sensitivity while effectively negating stretch-induced interference. Our findings are underpinned by an experimentally validated electromechanical model. In practical applications, SHRPS mounted on inflatable probes demonstrated safe and precise palpation on the human wrist and conformable and firm gripping of contoured objects. The debut of SHRPS promises to significantly expand the versatile applications of e-skins.