Emergency call-routing apparatus, and an associated method, for use in a packet-based, telephonic network. An emergency call router is positioned selectably to provide local call handling functionality to a local network that is normally connected by way of an access gateway to the telephonic network whose operation is normally controlled by a softswitch. The apparatus is used when, e.g., a total communication link failure condition occurs between the access gateway and the softswitch. The emergency call router selectably routes calls within the local network to permit continued, local calling functionality in spite of the failure of the communication link. High-priority calls, such as calls placed to an emergency dispatch center, are routed within the local network to a designated, local-network station. And local calls are also selectably routed by the emergency call router. A call priority scheme is also used in the event that call capacity is exceeded. Calls of higher priority are permitted while calls of lower priority are blocked.