A continuous-wave erbium-doped ytterbium-free fiber laser generates a record-breaking pump-power-limited output power of 656 W at ∼1601 nm when cladding pumped by 0.98 μm diode lasers. The slope efficiency was 35.6% with respect to launched pump power, and the beam quality factor (M2) was ∼10.5. This M2 value excludes a fraction ∼25% of the power that emerged from the cladding, which we attribute in part to mode coupling between the 146 μm core and 700 μm inner cladding. Whereas these parameters are adequate for in-band tandem pumping of Tm-doped fiber lasers, we predict that an output power of over 1 kW is possible through pumping with state-of-the-art 0.98 μm diode lasers, even with a smaller core that allows for improved beam quality.