The large absolute photonic bandgaps of two-dimensional (2D) anisotropic magnetic plasma photonic crystals with hexagonal and square lattices are obtained by introducing tellurium dielectric rods using the modified plane wave expansion method. Equations for calculating the band structures in the irreducible part of the first Brillouin zone are theoretically deduced. The modulation properties indicate that the location and bandwidth of the absolute photonic bandgaps (PBGs) could be tuned by filling factor, plasma frequency, and magnetic field. The effective tunable ranges and critical values of these parameters are found. These results could be helpful in designing 2D anisotropic PPCs with large absolute PBGs.