Urban growth in and around European cities affects multiple aspects of the environment including green spaces. On the one hand, many cities struggle with environmental problems, overcrowding and overuse resulting from high population densities. On the other hand, high densities result in better access to public green spaces, effective public transport, or less demand for resources. Consequently, finding a balance between density and high liveability in a green and sustainable urban environment is a major challenge for urban planning. Although many studies report and discuss the provision of green spaces in European cities, they fail to relate green space provision to the potential demand by urban dwellers, and to the extent differences can be detected between types of green. Against this background, this paper develops a systematic understanding of green space supply and its relation to the residential density of cities. In so doing, it detects turning points of green space supply in 905 European cities. The results show that green space supply is sensitive to the type of green space, population size and location of cities. Particularly the relation between residential density and the supply with urban green spaces covering parks, public gardens or cemeteries, indicate turning points: at certain residential densities the urban green space supply is decreasing. At a certain residential density, the urban green space supply is highest and cities have a high potential to optimize the balance between sustainability and liveability. However, there is no single optimal residential density. Rather, turning points are different between cities of different density and location in Europe and between different types of neighborhoods within cities. Therefore, different optimum values need to be defined sensitive to these characteristics. For most of the European cities, a decrease of population or built-area cannot be expected in the future. In this situation, the approach to identifying the turning points for green space supply as presented in this paper can be used as a comparative method. This informs green space policies for defining acceptable densities of urban development and corresponding standards for the provision of urban green space.