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In general, optical spatiotemporal solitons with phase singularities, known as optical vortex bullets, are unstable. In particular, it is very difficult to preserve a vortex structure of a propagating localized wave. In this paper we propose to introduce absorption to the model used for the process description. By means of numerical simulation we study the formation and propagation of an optical vortex bullet at different regimes. Our goal is to find the conditions of bullet stabilization.