Provision of an EUV mask whereby influence of EUV reflected light from an absorber film surface in the peripheral portion of a mask pattern region is suppressed at a time of carrying out EUV lithography; an EUV mask blank to be employed for producing the above EUV mask; and a process for producing the EUV mask blank. A process for producing a reflective mask blank for EUV lithography (EUVL), comprising alternately laminating a high refractive index film and a low refractive index film on a substrate to form a multilayer reflective film for reflecting EUV light and forming an absorber layer for absorbing EUV light on the multilayer reflective film, wherein the process further comprises after formation of the above multilayer reflective film, heating a portion of a surface of the multilayer reflective film outside a portion to be a mask pattern region in a reflective mask for EUV lithography produced by employing the reflective mask blank for EUV, to reduce the reflectivity of the heated portion of the surface of the multilayer reflective film for EUV light.