Surface nanoscale axial photonics (SNAP) microresonators, which are fabricated by nanoscale effective radius variation (ERV) of the optical fiber with subangstrom precision, can be potentially used as miniature classical and quantum signal processors, frequency comb generators, and ultraprecise microfluidic and environmental optical sensors. Many of these applications require the introduction of nanoscale ERV with a large contrast α, which is defined as the maximum shift of the fiber cutoff wavelength introduced per unit length of the fiber axis. The previously developed fabrication methods of SNAP structures, which used focused CO2 and femtosecond laser beams, achieved α∼0.02 nm∕μm. Here we develop a new, to the best of our knowledge, fabrication method of SNAP microresonators with a femtosecond laser, which allows us to demonstrate a 50-fold improvement of previous results and achieve α∼1 nm∕μm. Furthermore, our fabrication method enables the introduction of ERV that is several times larger than the maximum ERV demonstrated previously. As an example, we fabricate a rectangular SNAP resonator and investigate its group delay characteristics. Our experimental results are in good agreement with theoretical simulations. Overall, the developed approach allows us to reduce the axial scale of SNAP structures by an order of magnitude.