The method comprises, in the time domain, echo cancellation processing (40) by subtracting from the microphone signal a reference signal delivered by an adaptive circuit for modeling the acoustic coupling between the microphone (18) and the loudspeaker (16). Successive frames of the signal are subjected in the frequency domain to processing (42) for suppressing the residual echo that remains after the echo cancellation, together with noise reduction processing (44). The residual echo suppression processing comprises estimating respective values for the power of the residual echo over a plurality of defined frequency bands for successive signal frames, then calculating and applying a variable gain specific to each frequency band and to each frame, the respective gains being smaller whenever the estimated relative power of the residual echo is high for the frequency band under consideration, and vice versa. For each frequency band and for each frame, the respective values of the power of the ambient noise present in the microphone signal are estimated a priori, and the relative levels of the power of the noise and of the power of the residual echo in the microphone signal are compared. The variable gain is a function of the estimated relative power of the residual echo when its level is greater than that of the noise, and otherwise of the estimated relative power of the noise.