Key points Incomplete development of the neural circuits that control breathing contributes to respiratory disorders in pre‐term infants. Manifestations include respiratory instability, prolonged apnoeas and poor ventilatory responses to stimuli. Based on evidence suggesting that omega‐3 polyunsaturated fatty acids (n‐3 PUFA) improves brain development, we determined whether n‐3 PUFA supplementation (via the maternal diet) improves respiratory function in 10–11‐day‐old rat pups. n‐3 PUFA treatment prolonged apnoea duration but augmented the relative pulmonary surface area and the ventilatory response to hypoxia. During hypoxia, the drop in body temperature measured in treated pups was 1 °C less than in controls. n‐3 PUFA treatment also reduced microglia cell density in the brainstem. Although heterogeneous, the results obtained in rat pups constitute a proof of concept that n‐3 PUFA supplementation can have positive effects on neonatal respiration. This includes a more sustained hypoxic ventilatory response and a decreased respiratory inhibition during laryngeal chemoreflex. Abstract Most pre‐term infants present respiratory instabilities and apnoeas as a result of incomplete development of the neural circuits that control breathing. Because omega‐3 polyunsaturated fatty acids (n‐3 PUFA) benefit brain development, we hypothesized that n‐3 PUFA supplementation (via the maternal diet) improves respiratory function in rat pups. Pups received n‐3 PUFA supplementation from an enriched diet (13 g kg−1 of n‐3 PUFA) administered to the mother from birth until the experiments were performed (postnatal days 10–11). Controls received a standard diet (0.3 g kg−1 of n‐3 PUFA). Breathing was measured in intact pups at rest and during hypoxia (FiO2 = 0.12; 20 min) using whole body plethysmography. The duration of apnoeas induced by stimulating the laryngeal chemoreflex (LCR) was measured under anaesthesia. Lung morphology was compared between groups. Maternal n‐3 PUFA supplementation effectively raised n‐3 PUFA levels above control levels both in the blood and brainstem of pups. In intact, resting pups, n‐3 PUFA increased the frequency and duration of apnoeas, especially in females. During hypoxia, n‐3 PUFA supplemented pups hyperventilated 23% more than controls; their anapyrexic response was 1 °C less than controls. In anaesthetized pups, n‐3 PUFA shortened the duration of LCR‐induced apnoeas by 32%. The relative pulmonary surface area of n‐3 PUFA supplemented pups was 12% higher than controls. Although n‐3 PUFA supplementation augments apnoeas, there is no clear evidence of deleterious consequences on these pups. Based on the improved lung architecture and responses to respiratory challenges, this neonatal treatment appears to be beneficial to the offspring. However, further experiments are necessary to establish its overall safety.