We theoretically demonstrate that increase of absorption with constant gain in laser systems can lead to onset of laser generation. This counterintuitive absorption induced lasing (AIL) is explained by emergence of additional lasing modes created by an introduction of an absorbing medium with narrow linewidth. We show that this effect is universal and, in particular, can be encountered in simple Fabry-Perot-like systems and doped spherical dielectric nanoresonators. The predicted behavior is robust against detuning between the resonant frequencies of gain and absorbing medium.