A generalized energy principle is used to determine the effect of ion cyclotron resonant heating (lCRH) on the stability of m = 1 intemal kink displacements in the low-frequency limit: such displacements are associated with sawtooth oscillations. An integral expression is obtained for the contribution to the plasma energy of an ICRH-heated minority ion population with strong temperature anisotropy, which relates the former to the ICRH power input and its deposition profile. The link is provided by a realistic, but analytically tractable, new model for the distribution function of the heated ions, which is based on the approach of Stix [Nucl. Fusion 15, 737 (1975)]. Numerical evaluation of the integral expression is carried out using parameters inferred from ICRH experiments in the Joint European Torus (JET) [Campbell et aI., Phys. Rev. Lett. 60, 2148 (1988)]. It is shown that the ideal m = I internal kink is stable at values of the poloidal plasma beta f3 p which typically lie in the range 0.4-1, depending on the radio-frequency power input and the radius r 1 of the q = I surface.