Single-frequency fiber lasers (SFFLs), 1083 nm, have been extensively applied in 4He optical pumping magnetometers (OPMs) for magnetic field detection. However, the sensitivity and accuracy of OPMs are constrained by the frequency stability of SFFLs. Focusing on this concern, the frequency-stabilized performance of the 1083 nm SFFLs is successfully improved by externally tailoring the laser linewidth to match the spectral width of the error signal in saturated absorption spectroscopy. Thereinto, a high-intensity error signal of saturated absorption is generated as a large number of 4He atoms with a wide range of velocities interacting with the 1083 nm laser. Consequently, the root mean square value of the fluctuating frequency after locking is effectively decreased from 24.6 to 13.6 kHz, which achieves a performance improvement of 44.7%. Such a strategy can provide a technical underpinning for effectuating an absolute frequency stabilization with higher precision based on atomic and molecular absorption spectroscopy techniques.