Selenite compounds reveal unique properties such as multiferroicity, selective-ion exchange, and nonlinear optical properties. Previously we reported Li₁₃Mn(SeO₃)₈ showing dynamic Jahn-Teller distortion. In this research, we have synthesized two novel lithium transition metal selenite compounds, namely, Li₆Co(SeO₃)₄ and Li₆Ni(SeO₃)₄. Isostructural title compounds crystallize in a rhombohedral space group, R-3, and consist of Li⁺, CoO₆ (or NiO₆) octahedra, and SeO₃ polyhedra forming a three-dimensional distorted cubic lattice. The structure of the materials is closely related to that of Li₁₃Mn(SeO₃)₈: some of the Li⁺ cations in Li₁₃Mn(SeO₃)₈ have been substituted by transition metal cations and the oxidation state of the transition metals has been reduced from +3 to +2. The magnetic measurements indicate that Li₆Co(SeO₃)₄ is a canted antiferromagnet while Li₆Ni(SeO₃)₄ is an antiferromagnet. The antiferromagnetic interaction of the title compounds may be due to anisotropic interactions. Detailed structural description, spectroscopic analysis, and magnetic properties will be presented.