We demonstrate a compact extreme ultraviolet (XUV) source based on high-harmonic generation (HHG) driven directly inside the cavity of a mode-locked thin-disk laser oscillator. The laser is directly diode-pumped at a power of only 51 W and operates at a wavelength of 1034 nm and a 17.35 MHz repetition rate. We drive HHG in a high-pressure xenon gas jet with an intracavity peak intensity of 2.8×1013 W/cm2 and 320 W of intracavity average power. Despite the high-pressure gas jet, the laser operates at high stability. We detect harmonics up to the 17th order (60.8 nm, 20.4 eV) and estimate a flux of 2.6×108 photons/s for the 11th harmonic (94 nm, 13.2 eV). Due to the power scalability of the thin-disk concept, this class of compact XUV sources has the potential to become a versatile tool for areas such as attosecond science, XUV spectroscopy, and high-resolution imaging.