The addition of Ta (2-10 wt.%) to a starting mixture of Mg and B (taken in the MgB2 stoichiometry) and application of high pressure (2 GPa) during the synthesis process (800-900 degreesC for 1 h) allow us to produce bulk MgB2-based materials with the critical current densities (j(c)) of: 630 kA/cm(2) at 10 K, 425 kA/cm(2) at 20 K, 165 kA/cm(2) at 30 K in the 0 T field; 570 kA/cm(2) at 10 K, 350 kA/cm(2) at 20 K and 40 kA/cm(2) at 30 K in the 1 T field and 650 A/cm(2) at 10 K in the 10 T field. X-ray and SEM studies have shown that Ta did not react with B or Mg, but absorbed the impurity gases to form Ta2H, TaH, TaN0.1, etc. The samples with highest superconductive characteristics exhibited a reduced amount or absence of MgH2 in the Mg-B-O-matrix phase, as well as, the impurity nitrogen and oxygen in MgB2 single crystals distributed over the matrix. Samples with a higher level of critical currents included some amount of unreacted Mg. The Vickers microhardness of the matrix material was H-v = 12.54 +/- 0.86 GPa (at 0.496-N load). The nanohardness (at 60 mN load) of MgB2 single crystals located in the matrix was 35.6 +/- 0.9 GPa, i.e. higher than the nanohardness of sapphire (31.1 +/- 2.0 GPa), and that means that MgB2 belongs to superhard materials. (C) 2002 Elsevier Science B.V. All rights reserved.