Evolution of magnetism in single crystals of the van der Waals compound VI3 in external pressure up to 7.3 GPa studied by measuring magnetization and ac magnetic susceptibility is reported. Four magnetic phase transitions, at T1 = 54.5 K, T2 = 53 K, TC = 49.5 K, and TFM = 26 K, respectively have been observed at ambient pressure. The first two have been attributed to the onset of ferromagnetism in specific crystal-surface layers. The bulk ferromagnetism is characterized by the magnetic ordering transition at Curie temperature TC and the transition between two different ferromagnetic phases TFM, accompanied by a structure transition from monoclinic to triclinic symmetry upon cooling. The pressure effects on magnetic parameters were studied with three independent techniques. TC was found to be almost unaffected by pressures up to 0.6 GPa whereas TFM increases rapidly with increasing pressure and reaches TC at a triple point at ~ 0.85 GPa. At higher pressures, only one magnetic phase transition is observed moving to higher temperatures with increasing pressure to reach 99 K at 7.3 GPa. In contrast, the low-temperature bulk magnetization is dramatically reduced by applying pressure (by more than 50% at 2.5 GPa) suggesting a possible pressure-induced reduction of vanadium magnetic moment. We discussed these results in light of recent theoretical studies to analyze exchange interactions and provide how to increase the Curie temperature of VI3.