Abstract <p>This paper discusses the role of the interaction of pumping and lasing waves in a fiber laser with randomly distributed feedback due to weak Rayleigh backscattering, operating in the narrowband lasing mode observed when the pumping power slightly exceeds the threshold. In this case, the spectrum consists of narrow (less than 1 MHz) modes with a typical lifetime of 1 ms. Earlier, it has been demonstrated that both external noise (thermal or acoustic) and nonlinear four-wave interaction between the lasing modes can be responsible for the mode decomposition. A model of the nonlinear interaction of a pumping wave with an ultra-narrow lasing mode has been constructed to show that the phase cross-modulation between them can lead to the mode destruction if the wave divergence is sufficiently slow. It follows that the narrowband lasing mode depends on the fiber dispersion, since the latter governs the corresponding spread length. A comparison with experiment confirms this conclusion: no narrowband generation is observed in random lasers based on low-dispersion fibers, while it exists for fibers with a high dispersion coefficient.</p>