(Hg, Re)Ba₂Ca₂Cu₃O_8+δ ((Hg, Re)-1223) samples have been fabricated by wrapping Re_0.2Ba₂Ca₂Cu₃O_y precursor powder within Ag foil and pressing or rolling. The Ag/precursor composite is then reacted with CaHgO₂ in sealed reaction tubes. X-ray diffraction (XRD) patterns showed only one superconducting phase, (Hg, Re)-1223, in agreement with magnetization measurements showing an onset critical temperature (T_c) of 132 K. The magnetization properties were studied by dc magnetic measurements. The irreversibility line (H_irr), deduced from magnetization hysteresis loops, is approximated by a power law, H_irr ~ (1 − T/T_c)ⁿ, with n ~ 2.5, indicating moderate coupling between CuO₂ layers compared to YBa₂Cu₃O₇ (n ~ 1.5) and Bi/Tl-based superconductors (n ~ 5.5). The temperature dependence of the magnetization hysteresis loop width ΔM showed three regimes, dominated by weak links at low temperature (regime I), thermally activated depinning of vortices at intermediate temperature (regime II) and giant flux creep at high temperature (regime III), respectively. Two field dependences were found in the intragrain critical current density (J^mag_c) versus applied field at various temperatures: a weak one at lower temperature (≤50 K) and a stronger one at high temperature (≥65 K), indicating a transition from vortex lattice to vortex liquid in the tapes. The transport critical current density (J^tran_c) of ~3 × 10³ A cm⁻² at 4.2 K and self-field was comparable to those for bulk Hg-based superconductors, indicating granular nature of the samples, which was confirmed further by XRD, scanning electron microscopy (SEM) and magneto-optical imaging (MOI).