The influence of sawtooth oscillations on the power of a tokamak reactor is investigated. Depending on the operation mode, the role of sawteeth can qualitatively be different. In particular, bursts of fusion power during and immediately after sawtooth crashes are predicted for the mode with a flat plasma density profile n(r) and a peaked ion temperature profile T(r) when T(0) > 16 keV. The main factor responsible for the effect of sawteeth on fusion power is the changes in the radial profiles of the plasma parameters caused by both the enhanced diffusion after a crash and the incomplete reconstruction of the n(r) and T(r) profiles between crashes.