The qualitative behavior of the laser whose frequency is continuously tuned within time over which the pulse acts and a medium inside the cavity has bleaching, is studied by numerical simulation. The medium is modeled as a closed three–level system with ground state and intermediate metastable level. It is shown that in comparison with the situation without bleaching of the medium, the distortions of the temporal dependence of lasing intensity in the region of selective absorption are much more pronounced. It is found that the position of the dip in lasing power as well as the frequency and the amplitude of oscillations caused by a nonlinear laser response on nonadiabatic frequency scanning throughout the line of selective absorption nontrivially depend on the scanning speed. The regions of quasicontinuous lasing are found, in which the distortions of the absorption line profile are negligible.