In this paper we propose an API to pause and resume task execution depending on external events. We leverage this generic API to improve the interoperability between MPI synchronous communication primitives and tasks. When an MPI operation blocks, the task running is paused so that the runtime system can schedule a new task on the core that became idle. Once the MPI operation is completed, the paused task is put again on the runtime system's ready queue. We expose our proposal through a new MPI threading level which we implement through two approaches.The first approach is an MPI wrapper library that works with any MPI implementation by intercepting MPI synchronous calls, implementing them on top of their asynchronous counterparts. In this case, the task-based runtime system is also extended to periodically check for pending MPI operations and resume the corresponding tasks once MPI operations complete. The second approach consists in directly modifying the MPICH runtime system, a well-known implementation of MPI, to directly call the pause/resume API when a synchronous MPI operation blocks and completes, respectively.Our experiments reveal that this proposal not only simplifies the development of hybrid MPI+OpenMP applications that naturally overlap computation and communication phases; it also improves application performance and scalability by removing artificial dependencies across communication tasks. This work has been developed with the support of the European Union Horizon 2020 Programme through both the INTERTWinE project (agreement No. 671602) and the Marie Sk lodowska-Curie grant (agreement No. 749516); the Spanish Government through the Severo Ochoa Program (SEV-2015-0493); the Spanish Ministry of Science and Innovation (TIN2015-65316-P) and the Generalitat de Catalunya (2017-SGR-1414). Peer Reviewed