Applying an external static magnetic field to laser beam welding may lead to a change in geometry of the weld seam. Since the most common influence of a magnetic field acting on an electrically high conducting fluid is the generation of a Lorentz force, the outcome of such experiments is a strong indication of the presence of electric current in the melt pool. Owing to the static nature of the magnetic field, induction is restricted to the movement of the liquid metal and therefore negligible, leaving thermoelectricity as the sole potential source of current. The present work discloses analytically that the current may indeed originate from a gradient of thermoelectric power. Based on the examples iron and aluminum, key features of the current distribution are determined numerically together with an investigation of the dependence of the distribution on material properties. By carrying out welding experiments in the heat conduction mode, validation is achieved of the thermoelectric source of the current and of basic properties of its contribution.