  The finite nuclear size corrections to the relativistic recoil effect in
H-like ions are calculated within the Breit approximation. The calculations are
performed for the $1s$, $2s$, and $2p_{1/2}$ states in the range $Z =$ 1-110.
The obtained results are compared with previous evaluations of this effect. It
is found that for heavy ions the previously neglected corrections amount to
about 20% of the total nuclear size contribution to the recoil effect
calculated within the Breit approximation.
