The emergence of mega-constellations of interconnected satellites has a major impact on the integration of cellular wireless and non-terrestrial networks (NTN). This paper studies the problem of running a federated learning (FL) algorithm within a low Earth orbit (LEO) constellation of satellites connected with intra-orbit inter-satellite links (ISL). Satellites apply on-board machine learning and transmit the local parameters to the parameter server (PS). The main contribution is a novel approach to enhance FL in satellite constellations using intra-orbit ISLs. The key idea is to rely on the predictability of satellite visits to create a system design in which ISLs mitigate the impact of intermittent connectivity and transmit the aggregated parameters to the PS. We first devise a synchronous FL, which is then extended towards an asynchronous FL for the case of sparse satellite visits to the PS. An efficient use of the satellite resources is attained by sparsification-based compression the aggregated parameters of each orbit before forwarding to the PS. Performance is evaluated in terms of accuracy and the required size of data to be transmitted. The numerical results indicate a faster convergence rate of the presented approach compared with the state-of-the-art FL on satellite constellations.