The nominal (Hg1−xRex)Sr2CuO4+δ(x=0.10 and 0.20) samples were synthesized at ∼920°C in partial vacuum. The compound with x=0.10 exhibits superconductivity at ∼54K while the composition x=0.20 is non-superconducting down to 5K. On cooling below 10K in an applied field of 4kOe, the former causes a noticeable upturn in the field cooled (FC) magnetization signal.Such a change in magnetic response is also reflected in the magnetic hysteresis loop generated at 9 K. We attribute this effect to a paramagnetic contribution arising from Re in (Hg,Re)-1201 phase.