Apparatus for welding continuous strips (1a,1b) wound on a support ring (113), comprising at least means (2) for feeding the strips (1a,1b) to be wound on the support ring (113), an assembly (100) for winding said strips, an assembly (200) for applying radial pressure onto the strips, comprising a first circular jaw (211) and a second circular jaw (212), which are arranged opposite each other and spaced in the longitudinal direction (X-X) by an amount corresponding to the width of the finished seal, and an assembly (300) for welding one (1a) of said strips (1a,1b), said pressing assembly (200) and said welding assembly (300) being coaxial, wherein said welding assembly (300) comprises a first electrode (310) and a second electrode (320) which are arranged inside the jaws (211,212) of the pressing assembly so as to face each other and have a diameter smaller than that of the said jaws (211,212).