From flexible interconnection among feeders to hybrid alternating current (AC) and direct current (DC) distribution structures of future smart distribution systems, medium-voltage DC distribution centers with flexibly interlinked multiple microgrids (MGs) will have wide applications on the demand side. A generic coordinated control framework based on a distributed cooperation scheme is proposed for such DC centers, as opposed to centralized control structures. A novel unified control only using local measurements is proposed for these interlinking converters. During normal power disturbances, automatic coordinated power control and mutual support among subsystems can be realized, thereby improving DC voltage and AC frequency stability to enable multiple MGs to be treated as a real unified cluster. Moreover, with this method, interlinking converters can realize seamless transition in power dispatching mode, common DC bus voltage control mode, and MG support mode without communication and control system switching. A simplified dynamic model has been developed to verify the proposed control strategy. This work is expected to provide a new solution for flexible interconnection and operational control of large-scale MG clusters.