The Mg-Zn and Al-Zn binary alloys have been investigated theoretically under static isotropic pressure. The stable phases of these binaries on both initially hexagonal-close-packed (HCP) and face-centered-cubic (FCC) lattices have been determined by utilizing an iterative approach that uses a configurational cluster expansion method, Monte Carlo search algorithm, and density functional theory (DFT) calculations. Based on 64-atom models, it is shown that the most stable phases of the Mg-Zn binary alloy under ambient condition are $rm MgZn_3$, $rm Mg_{19}Zn_{45}$, $rm MgZn$, and $rm Mg_{34}Zn_{30}$ for the HCP, and $rm MgZn_3$ and $rm MgZn$ for the FCC lattice, whereas the Al-Zn binary is energetically unfavorable throughout the entire composition range for both the HCP and FCC lattices under all conditions. By applying an isotropic pressure in the HCP lattice, $rm Mg_{19}Zn_{45}$ turns into an unstable phase at P$approx$$10$~GPa, a new stable phase $rm Mg_{3}Zn$ appears at P$gtrsim$$20$~GPa, and $rm Mg_{34}Zn_{30}$ becomes unstable for P$gtrsim$$30$~GPa. For FCC lattice, the $rm Mg_{3}Zn$ phase weakly touches the convex hull at P$gtrsim$$20$~GPa while the other stable phases remain intact up to $approx$$120$~GPa. Furthermore, making use of the obtained DFT results, bulk modulus has been computed for several compositions up to pressure values of the order of $approx$$120$~GPa. The findings suggest that one can switch between $rm Mg$-rich and $rm Zn$-rich early-stage clusters simply by applying external pressure. $rm Zn$-rich alloys and precipitates are more favorable in terms of stiffness and stability against external deformation.
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