Animal social and spatial behaviours are inextricably linked. Animal movements are driven by environmental factors and social interactions. Habitat structure and changing patterns of animal space use can also shape social interactions. Animals adjust their social and spatial behaviours to reduce the risk of offspring mortality. In territorial infanticidal species, two strategies are possible for males: they can stay close to offspring to protect them against rivals (infant‐defence hypothesis) or patrol the territory more intensively to prevent rival intrusions (territorial‐defence hypothesis). Here, we tested these hypotheses in African lions ( Panthera leo ) by investigating how males and females adjust their social and spatial behaviours in the presence of offspring. We combined datasets on the demography and movement of lions, collected between 2002 and 2016 in Hwange National Park (Zimbabwe), to document the presence of cubs (field observations) and the simultaneous movements of groupmates and competitors (GPS tracking). We showed a spatial response of lions to the presence of offspring, with females with cubs less likely to select areas close to waterholes or in the periphery of the territory than females without cubs. In contrast, these areas were more selected by males when there were cubs in the pride. We also found social responses. Males spent more time with females as habitat openness increased but the presence of cubs in the pride did not influence the average likelihood of observing males with females. Furthermore, rival males relocated further after an encounter with pride males when cubs were present in the prides, suggesting that the presence of cubs leads to a more vigorous repulsion of competitors. Males with cubs in their pride were more likely to interact with male competitors on the edge of the pride's home range and far from the waterholes, suggesting that they are particularly assiduous in detecting and repelling rival males during these periods. In general, the strategies to avoid infanticide exhibited by male lions supported the territorial‐defence hypothesis. Our study contributes to answer the recent call for a behavioural ecology at the spatial‐social interface.