Ultraviolet microdisk lasers are integrated monolithically into photonic circuits using a III-nitride-on-silicon platform with gallium nitride (GaN) as the main waveguide layer. The photonic circuits consist of a microdisk and a pulley waveguide, terminated by out-coupling gratings. In this Letter, we measure quality factors up to 3500 under continuous-wave excitation. Lasing is observed from 374 to 399 nm under pulsed excitation, achieving low-threshold energies of 0.14mJ/cm2 per pulse (threshold peak powers of 35kW/cm2). A large peak-to-background dynamic of around 200 is observed at the out-coupling grating for small gaps of 50 nm between the disk and the waveguide. These devices operate at the limit of what can be achieved with GaN in terms of operation wavelength.