Using the compressible resistive magnetohydrodynamic (MHD) equations in a finite aspect ratio cylinder, it is found that them=1 mode (the sawtooth oscillation) can saturate when the pressure inside the magnetic island is higher than that of the original core plasma. The saturation condition is of the form &Dgr;&bgr;p≳8&egr;−1q=1(1−q0)2. This saturation effect can be used to actively stabilize sawteeth by heating or raising the density in the island. This mechanism, together with a stabilizing toroidal effect, may also explain recent lower‐hybrid wave‐driven tokamak experiments where the saturation of sawteeth has been observed.