Continuously tunable lasers with a narrow linewidth are at the core of a large number coherent optical systems. Integration of these devices on a single chip will enable a large number of applications that require minimal size, weight, power, and cost. In this work, we demonstrate a 3 nm-continuously tunable laser operating around 1550 nm with a narrow intrinsic linewidth of 5.7 kHz. The device is fully integrated on a siliconon-insulator platform and the optical gain is provided by a bonded III-V layer. The narrow laser linewidth is attained with an extended cavity that consists of a Vernier ring-based mirror and a passive waveguide. To reach the record continuous (mode-hopfree) tuning range of 3 nm (375 GHz), we demonstrate a method for synchronously tuning the Vernier resonances together with the cavity longitudinal modes, both thermally controlled. In the current laser, the mode-hop-free tuning range is limited by the maximum heating power, but it can be extended over more than 10 nm (1.25 THz) by optimizing the integrated heater design.