To explore effects of pressure on the magnitude of the influence of differences in molecular transport coefficients on turbulent flame speed ST, experiments with statistically spherical flame kernels expanding in homogeneous isotropic turbulence in a fan-stirred bomb were performed. Flame speeds were evaluated by analyzing flame images obtained using a high-speed Schlieren technique. To reach the study goals, the measurements were done at three different pressures (P = 1, 3, and 5 atm) with three different mixtures: (i) lean (the equivalence ratio π=0.45) H2/air mixture, (ii) lean (π=0.45) H2/O2/He mixture, and (iii) the stoichiometric CH4/air mixture. Mixtures (i) and (iii) are characterized by significantly different Lewis numbers (Le=0.35 and Le~1, respectively), approximately equal thermal laminar flame thicknesses δL, and close values of the laminar flame speed SL at the three pressures. Combustion chemistry is expected to be weakly affected by substitution of N2 in mixture (i) with He in mixture (ii), with this substitution increasing Le to 0.91, but the two mixtures are characterized by significantly different δL at the three pressures and different SL at P = 3 and 5 atm. Comparison of the normalized turbulent flame speeds ST/SL obtained from the lean H2/air flames and stoichiometric CH4/air flames shows that ST/SL is significantly higher in the former flames, with the difference being significantly increased by P. These experimental data indicate a substantial increase in the magnitude of the influence of differential diffusion effects on ST with pressure. An analysis of data obtained from the lean H2/O2/He flames further supports this conclusion. Based on results of numerical simulations of complex-chemistry laminar premixed flames, the pressure-dependence of the magnitude of the influence of differential diffusion effects on ST/SL is attributed to an increase in the Zel'dovich number by pressure, with the latter effect being most pronounced for the lean H2/O2/He mixture.