The effect of pressure on magnetic properties of LaCoO$_3$ is studied experimentally and theoretically. The pressure dependence of magnetic susceptibility $chi$ of LaCoO$_3$ is obtained by precise measurements of $chi$ as a function of the hydrostatic pressure $P$ up to 2 kbar in the temperature range from 78 K to 300 K. A pronounced magnitude of the pressure effect is found to be negative in sign and strongly temperature dependent. The obtained experimental data are analysed by using a two-level model and DFT+U calculations of the electronic structure of LaCoO$_3$. In particular, the fixed spin moment method was employed to obtain a volume dependence of the total energy difference $Delta$ between the low spin and the intermediate spin states of LaCoO$_3$. Analysis of the obtained experimental $chi(P)$ dependence within the two-level model, as well as our DFT+U calculations, have revealed the anomalous large decrease in the energy difference $Delta$ with increasing of the unit cell volume. This effect, taking into account a thermal expansion, can be responsible for the temperatures dependence of $Delta$, predicting its vanishing near room temperature.
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