We studied the pressure and temperature dependence of the electrical resist
ivity of the superconducting compound magnesium diboride (MgB2). The superc
onducting transition temperature decreases monotonically with pressure, bei
ng parabolic or linear, depending on samples. The rate of decrease under pr
essure is higher than in conventional superconductors. We discuss our resul
ts in terms of the semimetallic character of the electronic band structure
of MgB2.