An InP-based, monolithically integrated multiwavelength laser with optical feedback is presented. We demonstrate the performance of the dual-wavelength operation. Single-mode lasing is obtained for each of the two channels within a temperature range from 16 to $30$ °C and an injection current range from 30 to 70 mA without mode-hopping. This is due to the combined filtering functions of an arrayed waveguide grating and a distributed Bragg reflector. A method that makes use of weak optical feedback is demonstrated to improve the stability of each single-mode. With this method, sustained relaxation oscillations that are excited by on-chip parasitic reflections are damped and linewidths in both channels are narrowed to around 400 kHz compared to the linewidth of 1 MHz that is obtained when no feedback is applied. The suppression ratio of the relaxation-oscillation-induced side peaks is measured to be over 45 dB for two simultaneously operated channels.