We analyze, to the best of our knowledge, a new type of topological optical solitons in lasers with fast saturable absorption, which is intermediate between 2D and 3D ones. Being generated by 2D laser solitons, such 3D dissipative solitons in a laser cavity of length L have a number of vortex lines, which are straight for under-critical values L and spiral for larger L. For supercritical L, a vortex with multiple topological charges m>1 in generating 2D solitons transforms into m separate vortex lines. Taking into account weak non-paraxiality reveals polarization singularities in the form of lines, on which the elliptical polarization turns into linear in the cross section of the structures.