Superconducting MgB2 samples were prepared by the sintering of a mixture of fine Mg (or Mg alloy) powder produced by gas-atomization and B powder. The single MgB2 phase with a superconducting onset temperature of 38 K was obtained by sintering at 1073K for the pure Mg or AZ31 alloy powders. In the case of AZ31, the superconducting MgB2 was obtained by sintering at a low temperature of 873 K for 50 h although a long sintering time of 100h is needed to obtain a single MgB2 phase for Mg powder. This indicates that the AZ31 alloy enhances a formation rate of superconducting MgB2 at the low temperature through the formation of the partial melting phase. Thus, the gas-atomized fine Mg or AZ31 alloy powders are useful for preparation of a superconducting MgB2 and in particular AZ31 alloy is effective for the low temperature fabrication of MgB2.