Context. The first couple of stellar generations may have been massive, of order 100?M⊙, and to have played a dominant role in galaxy formation and the chemical enrichment of the early Universe. Some fraction of these objects may have died as pair-instability supernovae or gamma-ray bursts. The winds of these stars may have played an important role in determining these outcomes. As the winds are driven by radiation pressure on spectral lines, their strengths are expected to vary with metallicity. Until now, most mass-loss predictions for metal-poor O-type stars have assumed a scaled-down solar-abundance pattern. However, Population III evolutionary tracks show significant surface enrichment through rotational mixing of CNO-processed material, because even metal-poor stars switch to CNO-burning early on. Aims. We address the question of whether the CNO surface enhanced self-enrichment in the first few generations of stars could impact their mass-loss properties. Methods. We employ Monte Carlo simulations to establish the local line-force and solve for the momentum equation of the stellar outflow, testing whether an outflow can actually be established by assessing the net acceleration at the sonic point of the flow. Stellar evolution models of rotating metal-poor stars are used to specify the surface chemical composition, focussing on the phases of early enrichment. Results. We find that the mass-loss rates of CNO enhanced metal-poor stars are higher than those of non-enriched stars, but they are much lower than those rates where the CNO abundance is included in the total abundance Z. Metal-poor stars hotter than ?~50?000?K, in the metallicity range investigated here (with an initial metallicity Z???10-4) are found to have no wind, as the high-ionization species of the CNO elements have too few strong lines to drive an outflow. We present a heuristic formula that provides mass-loss estimates for CNO-dominated winds in relation to scaled-down solar abundances. Conclusions. CNO-enriched or not, the winds of metal-poor stars are generally found to be too weak to contribute significantly to the overall mass loss. Population III supernovae are thus expected to be responsible for the bulk of the early nucleo-synthetic enrichment, unless additional mass-loss mechanisms such as η?Carinae type eruptions or steady mass loss close to the Eddington/Omega limit is important.
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