Metal particles that can be alloyed with rhenium are dispersed as a main component in a gas phase, a rhenium oxide vapor is made to be present around these particles, the rhenium oxide is reduced, and the rhenium precipitated on the surface of the main component metal particles as a result of this reduction is diffused under a high temperature into the main component metal particles, which gives a rhenium-containing alloy powder including the main component metal and rhenium. The powder thus obtained preferably contains 0.01 to 50 wt % rhenium, has an average particle size of 0.01 to 10 .mu.m, and is made into a conductor paste by being uniformly mixed and dispersed in an organic vehicle along with other additives as needed.