We report the details of a technique for the production of proton beams with very low energy spread exploiting the short soft X-rays obtained by laser ablation. These beams have been generated by the dissociation and ionization of an hydrogen buffer gas induced by the laser-plasma X-rays and then accelerated by means of an electrostatic accelerator. Their properties have been analyzed through the time-of-flight method applying different accelerating voltages. The resulting energetic spread ranges between 6 and 11%, as a function of the applied voltage. Such a system could be extremely useful for producing quasi-monoenergetic proton beams.