A method for manufacturing a three-dimensional object, wherein planar layers (C1, C2, C3) are produced one after another such that each newly produced layer is superimposed, along a first axis that is perpendicular to the respective planes of the layers, on a layer previously produced or, if the latter is not present, on a planar metal support that is perpendicular to the first axis, each of these layers being made up of at least one metal strip (F1C1, F2C1, F1C2, F2C2, F3C2, F1C3, F2C3) such that the or each strip of each layer occupies the entire thickness, along the first axis, of the corresponding layer, characterized in that the method provides, to produce each layer (C1, C2, C3): - carrying out a deposition step, during the entire duration of which a part (F1C1.1) of the or each strip (F1C1, F2C1, F1C2, F2C2, F3C2, F1C3, F2C3) of the layer to be produced is pressed, along the first axis, in contact against the layer previously produced or, if the latter is not present, against the support; - carrying out a fusion step, which is done during the deposition step and during which only a portion (F1C1.1.F), called fused, of said part of the or each strip is welded by fusion to the layer previously produced or, if the latter is not present, the support, such that, at the end of this fusion step, the rest (F1C1.1.NF) of said part, which has not been fused, includes the edges (F1C1.1A, F1C1.1B, F1C1.1C) of said part, arranged transversely to the plane of the layer to be produced, and is still in contact with the layer previously produced or, if the latter is not present, the support; and - repeating said deposition and fusion steps several times by applying them to as many corresponding parts (F1C1.2) of the or each strip, which are offset from one another in a second axis perpendicular to the first axis, such that the fused portions (F1C1.1.F, F1C1.2.F) of two of said parts following one another in the second axis overlap, so that all of the fused portions that are obtained after having repeated the deposition and fusion steps relative to the strip(s) jointly form a two-dimensional section of the object to be manufactured. - carrying out a deposition step, during the entire duration of which a part (F1C1.1) of the or each strip (F1C1, F2C1, F1C2, F2C2, F3C2, F1C3, F2C3) of the layer to be produced is pressed, along the first axis, in contact against the layer previously produced or, if the latter is not present, against the support; - carrying out a fusion step, which is done during the deposition step and during which only a portion (F1C1.1.F), called fused, of said part of the or each strip is welded by fusion to the layer previously produced or, if the latter is not present, the support, such that, at the end of this fusion step, the rest (F1C1.1.NF) of said part, which has not been fused, includes the edges (F1C1.1A, F1C1.1B, F1C1.1C) of said part, arranged transversely to the plane of the layer to be produced, and is still in contact with the layer previously produced or, if the latter is not present, the support; and - repeating said deposition and fusion steps several times by applying them to as many corresponding parts (F1C1.2) of the or each strip, which are offset from one another in a second axis perpendicular to the first axis, such that the fused portions (F1C1.1.F, F1C1.2.F) of two of said parts following one another in the second axis overlap, so that all of the fused portions that are obtained after having repeated the deposition and fusion steps relative to the strip(s) jointly form a two-dimensional section of the object to be manufactured.