We report high-resolution angle-resolved photoemission measurements on single crystals of Pt_{2}HgSe_{3} grown by high-pressure synthesis. Our data reveal a gapped Dirac nodal line whose (001) projection separates the surface Brillouin zone in topological and trivial areas. In the nontrivial k-space range, we find surface states with multiple saddle points in the dispersion, resulting in two van Hove singularities in the surface density of states. Based on density-functional theory calculations, we identify these surface states as signatures of a topological crystalline state, which coexists with a weak topological phase.