The nonlinear dynamics of a high-power femtosecond singular pulse in Kerr media are analyzed numerically upon optically induced ionization. We examine the plasma inertia impact to stable propagation of optical vortices. Multifoci behavior of vortices in medium are revealed. Next we numerically demonstrate that inertial character of plasma formation provides a quasi-soliton regime of vortex propagation resistant to symmetry-breaking perturbation.