Robust localization of self-reproducing autocatalytic chemistries is a key step in the realization of heritable and evolvable chemical systems. While autocatalytic chemical reaction networks already possess attributes such as heritable self-reproduction and evolvability, localizing functional multispecies networks within complex primitive phases, such as coacervates, has remained unexplored. Here, we show the self-reproduction of the Azoarcus ribozyme system within charge-rich coacervates where catalytic ribozymes are produced by the autocatalytic assembly of constituent smaller RNA fragments. We systematically demonstrate the catalytic assembly of active ribozymes within phase-separated coacervates-both in micron-sized droplets as well as in a coalesced macrophase, underscoring the facility of the complex, charge-rich phase to support these reactions in multiple configurations. By constructing multispecies reaction networks, we show that these newly assembled molecules are active, participating both in self- and cross-catalysis within the coacervates. Finally, due to differential molecular transport, these phase-separated compartments endow robustness to the composition of the collectively autocatalytic networks against external perturbations. Altogether, our results establish the formation of multispecies self-reproducing reaction networks in phase-separated compartments which in turn render transient robustness to the network composition.