The layered perovskite Ca2RuO4 is a spin-one Mott insulator at ambient pressure and exhibits metallic ferromagnetism at least up to ~ 80 kbar with a maximum Curie temperature of 28 K. Above ~ 90 kbar and up to 140 kbar, the highest pressure reached, the resistivity and ac susceptibility show pronounced downturns below ~ 0.4 K in applied magnetic fields of up to ~10 mT. This indicates that our specimens of Ca2RuO4 are weakly superconducting on the border of a quasi-2D ferromagnetic state.