A more than tenfold increase in the intensity of EUV radiation from a laser-produced plasma source is observed experimentally under the illumination of a Xe gas-jet target with a wide laser beam covering its densest part compared with the radiation intensity at the traditional geometry, when the beam is sharply focused on the jet axis. As an explanation, it is assumed that in this case almost the whole dense part of the jet is heated and ionized under the action of laser irradiation and becomes transparent to the quanta of the studied radiation. The thickness of the absorbing peripheral shell of a laser spark decreases accordingly, that leads to the increase in the radiation intensity reaching the observer.