We have experimentally studied fundamental mode propagation in few meters long, adiabatically tapered step-index fibers with high numerical aperture, core diameter up to 117 μm (V = 38) and tapering ratio up to 18. The single fundamental mode propagation was confirmed by several techniques that reveal no signature of higher-order mode excitation. It can be, therefore, concluded that adiabatic tapering is a powerful method for selective excitation of the fundamental mode in highly multimode large-mode-area fibers. Annular near field distortion observed for large output core diameters was attributed to built-in stress due to thermal expansion mismatch between core and cladding materials. The mechanical stress could be avoided by an appropriate technique of fiber preform fabrication and drawing, which would prevent the mode field deformation and lead to reliable diffraction-limited fundamental mode guiding for very large core diameters.