To compensate widening of the central light spot which inevitably arises at linear polarization of a beam illuminating high-numerical-aperture axicon we propose to introduce an asymmetry in axicon structure. Experimental research of diffraction of Gaussian beam by three types of binary microaxicons with the period close to wavelength was carried out by means of near-field microscope. Diffractive optical elements with the period of 500 nanometers and various height of a microrelief have been fabricated by e-beam lithography. Narrowing of a central light spot formed by asymmetric microaxicons was experimentally confirmed. Overcoming of the diffraction limit (down to FWHM = 0.32λ) was observed in a near zone.