The possibility of passive and active burn stabilization of ignited deuterium-tritium (D-T) tokamak plasmas allowing for radial motion is studied by using a zero-dimensional transport model. Analyses are based on a linear stability method and a nonlinear dynamic simulation. The results are principally given for a self-ignited International Thermonuclear Experimental Reactor (ITER)-grade plasma. The radial motion has a stabilizing effect in a plasma with ITER89 scaling. It is impractical, however, to expect the radial motion to passively stabilize the burning plasma. A compression-decompression scheme based on regulation of the vertical field sufficiently stabilizes the plasma with ITER89 scaling. This control scheme requires some space for radial motion. The radial space requirement needed to manage a certain temperature perturbation is typically written as δR/R0 ≈ 0.6δT/T0. The allowable magnitude of temperature perturbation is within only 0.5% for δR = 2 cm. The extra space requirement would be the most severe problem in this control scheme. If the fraction GT of alpha-particle power loss due to field ripple is significant, the requirement on radial space might be considerably relaxed. Preliminary calculations have shown that δR/R0 ≈ 0.3δT/T0 might be achievable for GT = 20%.