Multi-wavelength sources are very attractive for optical telecommunication applications. Recently, several proposals have been made to use a frequency-shifting element inside a fiber laser ring cavity to realize a continuous wave (CW) multi-wavelength source operating at room temperature. In this type of laser, the frequency shift, introduced by an acousto-optic device, prevents the single frequency emission expected from the usual homogenous gain broadening behaviour of erbium-doped fiber. However, it has been previously observed that these sources can emit pulsed or CW radiation. In this paper, we describe the different emission regimes and we experimentally examine the impact of several key parameters on the optimization of the CW emission. To this end, a temporal characterization of the laser output was performed as a function of the cavity length, the number of simultaneously lasing wavelengths, the cavity loss, the erbium doped fiber length and the pump power. We found that an important parameter was the optical intensity circulating in the cavity. Indeed, the accumulated nonlinear phase shift and the amplifier saturation level are directly related to the intra-cavity laser field. By increasing the cavity loss or the number of wavelengths, the CW emission can be favoured over the mode-locked emission regime.