We report on the fabrication of micro-axicons made of glass by laser-assisted wet etching (LAE) and laser polishing. The employed technique, relying on a direct-writing process using a femtosecond laser, allows revealing high fidelity profiles when the exposed glass samples are etched in a heated potassium hydroxide (KOH) solution. The remaining surface roughness is then decreased by carbon dioxide (CO2) laser polishing. Such polishing is limited to the superficial layer of the component so that the tip is only slightly rounded, with a radius of curvature of nearly 200 µm. It is then shown with 500 µm-diameter axicons that a quasi-Bessel beam is generated closely after the tip and features a 5.3 µm diameter maintained over a propagation distance of almost 3.5 mm.