Defects are ubiquitous in solids and often introduce new properties that are absent in pristine materials. One of the opportunities offered by these crystal imperfections is an extrinsically induced long-range magnetic ordering(1), a long-time subject of theoretical investigations(1-3). Intrinsic, two-dimensional (2D) magnetic materials(4-7) are attracting increasing attention for their unique properties, which include layer-dependent magnetism(4) and electric field modulation(6). Yet, to induce magnetism into otherwise non-magnetic 2D materials remains a challenge. Here we investigate magneto-transport properties of ultrathin PtSe2 crystals and demonstrate an unexpected magnetism. Our electrical measurements show the existence of either ferromagnetic or antiferromagnetic ground-state orderings that depends on the number of layers in this ultrathin material. The change in the device resistance on the application of a similar to 25 mT magnetic field is as high as 400 Omega with a magnetoresistance value of 5%. Our first-principles calculations suggest that surface magnetism induced by the presence of Pt vacancies and the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange couplings across ultrathin films of PtSe2 are responsible for the observed layer-dependent magnetism. Given the existence of such unavoidable growth-related vacancies in 2D materials(8,9), these findings can expand the range of 2D ferromagnets into materials that would otherwise be overlooked.