Process for purifying a gas containing hydrogen sulfide, optionally with carbon dioxide, particularly adapted to the purification of gases of relatively low hydrogen sulfide content, e.g. not in excess of 1% of H.sub.2 S by volume, comprising contacting the gas with an absorption mass containing copper, at a temperature of from 250.degree. to 550.degree. C., to absorb the hydrogen sulfide and form copper sulfide; wherein the absorption mass is regenerated by interrupting the contact of the gas with the mass when the mass is at least partially saturated, contacting the mass with an oxidizing gas containing from 0.5 to 5% by volume of oxygen, at a temperature of from 250.degree. to 345.degree. C., to convert the copper sulfide substantially to copper sulfate, and then contacting the mass with a reducing gas containing from 5 to 20% by volume of hydrogen, at a temperature of from 300.degree. to 450.degree. C., to convert the copper sulfate substantially to sulfur dioxide and metallic copper, thereby regenerating the mass, which is then contacted again by the hydrogen sulfide containing gas.