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 thermally treated, 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 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), comprising two axes of rotation (θ, ω) of the axis of the laser beam incident on the working surface, which are perpendicular to one another, and an axis of translation (α) of the laser spot along said axis, and 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, said nozzles being arranged on said frame in such a way that longitudinal axes thereof form an angle of inclination (β) with respect to said vertical axis such that jets of said nozzles intersect in a powder-deposition point, said lower portion being configured for rotating said frame about a frame axis (ζ) parallel to a vertical axis of said first system of cartesian axes (X, Y, Z), 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,said laser operating machine comprising a numeric-control unit configured for managing control of actuators of the movement structure, of the optical system, as well as of an actuator that drives rotation about the frame axis (ζ) of the frame, said unit being configured to control said actuators of said moving element for moving said tool-carrier frame in a mobile way with respect to said optical assembly, rotating said frame in such a way that all the axes of the nozzles 34, or their projection on the working surface, at every moment do not intercept a direction of advance of a working segment. an upper portion fixedly associated to said movement structure, 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), comprising two axes of rotation (θ, ω) of the axis of the laser beam incident on the working surface, which are perpendicular to one another, and an axis of translation (α) of the laser spot along said axis, and 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, said nozzles being arranged on said frame in such a way that longitudinal axes thereof form an angle of inclination (β) with respect to said vertical axis such that jets of said nozzles intersect in a powder-deposition point, said lower portion being configured for rotating said frame about a frame axis (ζ) parallel to a vertical axis of said first system of cartesian axes (X, Y, Z), 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,said laser operating machine comprising a numeric-control unit configured for managing control of actuators of the movement structure, of the optical system, as well as of an actuator that drives rotation about the frame axis (ζ) of the frame, said unit being configured to control said actuators of said moving element for moving said tool-carrier frame in a mobile way with respect to said optical assembly, rotating said frame in such a way that all the axes of the nozzles 34, or their projection on the working surface, at every moment do not intercept a direction of advance of a working segment.