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We report the development of a compact, high-power, continuous-wave, single-frequency, ultraviolet (UV) source with extended wavelength tunability. The device is based on single-pass, intracavity, second-harmonic-generation (SHG) of the signal radiation of a singly resonant optical parametric oscillator (SRO) working in the visible and near-IR wavelength range. The SRO is pumped in the green with a 25-mm-long, multigrating, MgO doped periodically poled stoichiometric lithium tantalate (MgO:sPPLT) as nonlinear crystal. Using three grating periods, 8.5, 9.0, and 9.5 μm of the MgO:sPPLT crystal and a single set of cavity mirrors, the SRO can be tuned continuously across 710.7-836.3 nm in the signal and corresponding idler across 2115.8-1462.1 nm with maximum idler power of 1.9 W and maximum out-coupled signal power of 254 mW. By frequency-doubling the intracavity signal with a 5-mm-long bismuth borate (BIBO) crystal, we can further tune the SRO continuously over 62.8 nm across 355.4-418.2 nm in the UV with maximum single-frequency UV power, as much as 770 mW at 398.28 nm in a Gaussian beam profile. The UV radiation has an instantaneous line-width of ∼14.5  MHz and peak-peak frequency stability of 151 MHz over 100 s. More than 95% of the tuning range provides UV power >260  mW. Access to lower UV wavelengths can in principle be realized by operating the SRO in the visible using shorter grating periods.