Notwithstanding the limited commercial success of the first narrowband low earth orbit (LEO) satellite systems, the interest of the scientific community in this type of systems has been revived on the basis of the current trend toward the migration to all IP-based services. LEO systems can play a pivotal role in providing services to areas where there is no substantial terrestrial infrastructure. Above all, LEO satellite systems can be used as backbone networks to interconnect autonomous systems worldwide. Such an approach provides flexibility in managing the resulting integrated network infrastructure and supporting innovative applications. In this context, routing data from the source all the way to the destination constitutes a daunting challenge. In this paper, a location-assisted on-demand routing (LAOR) protocol is proposed and evaluated. The proposed protocol introduces for the first time in satellite systems the concept of on-demand routing. However, its implementation is tailored to the requirements imposed by the characteristics of the topology of LEO satellite systems. The performance of the LAOR protocol is assessed for different link-cost metrics and compared to the one of centralized routing protocols proposed in the literature so far. Simulation studies further document and confirm the positive characteristics of the proposed protocol.