[en] The m=1 (poloidal mode number) and n=1 (toroidal mode number) kinetic internal kink (KIK) mode in the presence of a density gradient is studied with the cylindrical version of the gyro-reduced MHD code, which is one of the extended MHD codes being able to treat the physics beyond resistive MHD. Electron inertia and electron finite temperature effects are included. The unstable KIK mode is observed in the parameter range in which the linear theory predicts complete stabilization due to the electron diamagnetic effect. The electrostatic potential profile in the linear stage of the KIK instability has the sheared poloidal flow with the m=1 mode structure. The vortexes are generated due to the Kelvin-Helmholtz (K-H) instability. The KIK is stabilized when the vortexes are formed, but it is destabilized again as the vortexes diminish due to the charge neutralizing electron motion along the magnetic field. These phenomena are observed in the early nonlinear stage of the KIK instability in which the width of the m=1 magnetic island is sufficiently small compared with the radial extent of the vortexes. The strong coupling between the vortexes and the KIK instability can be one of the candidates explaining the sudden onset of the sawtooth crash. (author)