This invention relates to a container pre-cutting system, applicable to multilayer and/or single-layer (3) container forming machines (4) that provide intermittent advances to the multi-layer and/or single-layer material with a length according to an advance step of the machine; said system being suitable for making a lower pre-cut (32) on the lower surface and an upper pre-cut (32) on the upper surface of the multilayer and/or single-layer material (3). The system comprises a lower pre-cutting device (1) and an upper pre-cutting device (2), provided with respective lower (11) and upper (21) blades having relative vertical movement with respect to the multilayer and/or single-layer material (3); and wherein the lower pre-cutting device (1) and the upper pre-cutting device (2) are separated in the advance direction of the multilayer and/or single-layer material (3) at a length approximately equal to a multiple of the advance step of the machine.