A laser operating machine for additive manufacture of objects, via a process of laser thermal treatment of metal powders, in particular via fusion, comprising a movement structure, which is mobile in a working space that comprises a working surface, said machine operating according to a first cartesian system of axes of movement (X, Y, Z) and being configured for supporting a moving element that comprises a plurality of nozzles for emitting jets of powder to be treated thermally, a working substrate (100, 110), and an optical laser assembly for conveying a laser beam to form a laser spot focused on said working substrate (100, 110) in order to carry out thermal treatment on said powders, wherein said moving element comprises: an upper portion fixedly associated to said movement structure, said optical laser assembly being set in said upper portion; a lower portion, comprising a duct on a end of which, giving out onto the working surface, is arranged a tool-carrier frame, arranged on which are said plurality of nozzles for emitting jets of powder, and in that said nozzles are arranged on said frame so that longitudinal axes thereof form an angle of inclination (β) with respect to a vertical axis such that jets of said nozzles intersect in a powder-deposition point, said optical laser assembly being set in the moving element so as to send the laser beam onto the working surface passing within a perimeter defined by said plurality of nozzles for emitting jets of powder, said optical assembly being configured for sending the laser beam through said duct and subsequently within the perimeter of the nozzles, on said tool-carrier frame, which in particular has a circular shape, said optical laser assembly comprising optical-scanning means for positioning said laser spot in the working space, which operate according to a respective set of axes of movement (α, θ, ω), characterised in said machine comprising actuator means for varying said angle of inclination (β) of said longitudinal axes of said one or more nozzles, the nozzles being fixed in a rotatable way, via rotation pins fixed on the frame, so as to be able rotate about an axis substantially tangential to the perimeter of the frame in such a way that only the angle of inclination (β) with respect to the vertical axis is varied, said actuator means comprising rotary actuators for rotating the nozzles about an axis tangential to the tool-carrier frame, the nozzles being arranged on said frame so that said rotation about an axis tangential to the tool-carrier frame includes at least a position in which the nozzles intercept the laser beam positioned by said optical-scanning means. an upper portion fixedly associated to said movement structure, said optical laser assembly being set in said upper portion; a lower portion, comprising a duct on a end of which, giving out onto the working surface, is arranged a tool-carrier frame, arranged on which are said plurality of nozzles for emitting jets of powder, and in that said nozzles are arranged on said frame so that longitudinal axes thereof form an angle of inclination (β) with respect to a vertical axis such that jets of said nozzles intersect in a powder-deposition point, said optical laser assembly being set in the moving element so as to send the laser beam onto the working surface passing within a perimeter defined by said plurality of nozzles for emitting jets of powder, said optical assembly being configured for sending the laser beam through said duct and subsequently within the perimeter of the nozzles, on said tool-carrier frame, which in particular has a circular shape, said optical laser assembly comprising optical-scanning means for positioning said laser spot in the working space, which operate according to a respective set of axes of movement (α, θ, ω), characterised in said machine comprising actuator means for varying said angle of inclination (β) of said longitudinal axes of said one or more nozzles, the nozzles being fixed in a rotatable way, via rotation pins fixed on the frame, so as to be able rotate about an axis substantially tangential to the perimeter of the frame in such a way that only the angle of inclination (β) with respect to the vertical axis is varied, said actuator means comprising rotary actuators for rotating the nozzles about an axis tangential to the tool-carrier frame, the nozzles being arranged on said frame so that said rotation about an axis tangential to the tool-carrier frame includes at least a position in which the nozzles intercept the laser beam positioned by said optical-scanning means.