Parametric interactions among three electrostatic waves in a magnetized plasma are investigated taking into account the finite Larmor radius (FLR) effect on the electron quiver velocity, which arises due to the finite wavelength of the electrostatic pump. It is found that the threshold is enhanced and the growth rates diminished. The changes in both quantities caused by the FLR effect compared with the values corresponding to the zero Larmor radius approximation are O(k02re2). Harmonic waves, the frequencies of which are the pump frequency, are also generated by shifted multiples of the electron gyrofrequency if the FLR effect is included. A higher-order parametric interaction driven by a harmonic wave is also investigated to find the threshold and growth rate for this instability.