Context : Aims : The bright M2.5 dwarf K2-18 ( M _ { s } = 0.36 M _ { \odot } , R _ { s } = 0.41 R _ { \odot } ) at 34 pc is known to host a transiting super-Earth-sized planet orbiting within the star ’ s habitable zone ; K2-18b . Given the superlative nature of this system for studying an exoplanetary atmosphere receiving similar levels of insolation as the Earth , we aim to characterize the planet ’ s mass which is required to interpret atmospheric properties and infer the planet ’ s bulk composition . Methods : We obtain precision radial velocity measurements with the HARPS spectrograph and couple those measurements with the K2 photometry to jointly model the observed radial velocity variation with planetary signals and a radial velocity jitter model based on Gaussian process regression . Results : We measure the mass of K2-18b to be 8.0 \pm 1.9 M _ { \oplus } with a bulk density of 3.7 \pm 0.9 g/cm ^ { 3 } which may correspond to a predominantly rocky planet with a significant gaseous envelope or an ocean planet with a water mass fraction \gtrsim 50 % . We also find strong evidence for a second , warm super-Earth K2-18c ( m _ { p,c } \sin { i _ { c } } = 7.5 \pm 1.3 M _ { \oplus } ) at \sim 9 days with a semi-major axis \sim 2.4 times smaller than the transiting K2-18b . After re-analyzing the available light curves of K2-18 we conclude that K2-18c is not detected in transit and therefore likely has an orbit that is non-coplanar with the orbit of K2-18b . A suite of dynamical integrations are performed to numerically confirm the system ’ s dynamical stability . By varying the simulated orbital eccentricities of the two planets , dynamical stability constraints are used as an additional prior on each planet ’ s eccentricity posterior from which we constrain e _ { b } < 0.43 and e _ { c } < 0.47 at the level of 99 % confidence . Conclusions : The discovery of the inner planet K2-18c further emphasizes the prevalence of multi-planet systems around M dwarfs . The characterization of the density of K2-18b reveals that the planet likely has a thick gaseous envelope which along with its proximity to the Solar system makes the K2-18 planetary system an interesting target for the atmospheric study of an exoplanet receiving Earth-like insolation .