[en] The dependence of the superconducting transition temperature T_c(P) on purely hydrostatic pressure to 0.9 GPa has been determined in ac susceptibility studies in a He-gas pressure system for optimally doped ceramic samples of HgBa₂CaCu₂O_6+δ and HgBa₂Ca₂Cu₃O_8+δ with superconducting transitions at T_c(0) ≅ 126.6 K and 133.9 K, respectively. T_c increases reversibly under hydrostatic pressure at the rates, d T_c/dP ≅ +1.80 ± 0.06 K/GPa and +1.71 ± 0.05 K/GPa, respectively. Within experimental error, these values are the same as found previously for optimally doped single-layered HgBa₂CuO_4+δ, where d T_c/dP ≅ +1.72 ± 0.05 K/GPa. Remarkably, the logarithmic volume derivative of T_c is nearly identical for all three compounds, dln T_c/dlnV ≅ -1.20 ± 0.05, even though the bulk modulus differs by more than 30%. This provides strong evidence that a common mechanism is responsible for the pressure dependence of the superconducting state in all three compounds