Silica waveguides with diameters larger than the wavelength of transmitted light are widely used in optical communications, sensors and other applications. Minimizing the width of the waveguides is desirable for photonic device applications, but the fabrication of low-loss optical waveguides with subwavelength diameters remains challenging because of strict requirements on surface roughness and diameter uniformity. Here we report the fabrication of subwavelength-diameter silica wires for use as low-loss optical waveguides within the visible to near-infrared spectral range. We use a two-step drawing process to fabricate long free-standing silica wires with diameters down to 50 nm that show surface smoothness at the atomic level together with uniformity of diameter. Light can be launched into these wires by optical evanescent coupling. The wires allow single-mode operation, and have an optical loss of less than 0.1 dB/mm. We believe that these wires provide promising building blocks for future microphotonic devices with subwavelength-width structures.