The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states that admit a fully local hidden variable model, i.e., where all parties are separated. Hence, although these states exhibit the strongest form of multipartite entanglement, they cannot lead to Bell inequality violation considering general nonsequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing genuine multipartite hidden nonlocality.