  A detailed magnetization study for the novel FeSe superconductor is carried
out to investigate the behavior of the intrinsic magnetic susceptibility $\chi$
in the normal state with temperature and under hydrostatic pressure. The
temperature dependencies of $\chi$ and its anisotropy $\Delta
\chi=\chi_{|}-\chi_{\bot}$ are measured for FeSe single crystals in the
temperature range 4.2-300 K, and a substantial growth of susceptibility with
temperature is revealed. The observed anisotropy $\Delta \chi$ is very large
and comparable with the averaged susceptibility at low temperatures. For a
polycrystalline sample of FeSe, a significant pressure effect on $\chi$ is
determined to be essentially dependent on temperature. Ab initio calculations
of the pressure dependent electronic structure and magnetic susceptibility
indicate that FeSe is close to magnetic instability with dominating enhanced
spin paramagnetism. The calculated paramagnetic susceptibility exhibits a
strong dependence on the unit cell volume and especially on the height $Z$ of
chalcogen species from the Fe plane. The change of $Z$ under pressure
determines a large positive pressure effect on $\chi$ which is observed at low
temperatures. It is shown that the literature experimental data on the strong
and nonmonotonic pressure dependence of the superconducting transition
temperature in FeSe correlate qualitatively with calculated behavior of the
density of electronic states at the Fermi level.
