This paper reports on the mode-locked operation of a 980-nm external-cavity passively mode-locked laser with extremely narrow RF linewidth. Optical pulses with 10-ps pulse duration were generated at a repetition rate of 955 MHz, with an average output power of 39.3 mW - which corresponds to a peak power of 4.1 W, generated directly from the oscillator. The RF spectrum displays a -3dB RF linewidth of only ∼40 Hz, as well as a 60-dB dynamic contrast, revealing the exceptionally low-noise fundamental mode-locked operation of this laser. At a repetition rate of ∼1 GHz, the highest peak power of 5.26 W was achieved, albeit with an increased -3dB RF linewidth of ∼100 Hz. The twosection chip incorporated an active region with a dual InGaAs quantum well sandwiched by an asymmetrical waveguide, and was operated at room temperature. By taking advantage of the broad tunability of the repetition rate which externalcavity lasers can afford, we also investigated the limits of stable fundamental mode-locked operation at the lowest repetition rates (or maximum external cavity lengths).