For La1–xPrxCoO3 cobaltites (x = 0, 0.1, 0.2, and 0.3), the dependence of magnetic susceptibility χ(T) is studied in the temperature range 5–400 K. Also, the crystal structure of these cobaltites is investigated, and the effect of pressure up to 2 kbar on their susceptibility is measured at T=78, 150, and 300 K. The specific dependencies χ(T) and the large negative pressure effect are assumed to arise from Co3+ ions contribution to the total susceptibility evaluated using La1−xPrxAlO3 as a reference system. The obtained experimental data on temperature and pressure effects in magnetism are analyzed within a two‐level model with energy gap Δ between the ground state of the system with zero spin of Co3+ ions and the excited higher‐spin state. In this model, magnetism of Co3+ ions is determined by the temperature‐induced population of the excited state, and magnitude of the pressure effect is governed by the volume dependence of Δ. The results of the analysis, supplemented by the theoretical calculations of the electronic structures of LaCoO3 and PrCoO3, indicate significant increase in Δ with decrease in the unit cell volume both under hydrostatic pressure and by substituting La with Pr having a smaller ionic radius.