This study addresses the end-to-end congestion control support over the DiffServ Assured Forwarding (AF) class. The resulting Assured Service (AS) provides a minimum level of throughput guarantee. In this context, this paper describes a new end-to-end mechanism for continuous transfer based on TCP-Friendly Rate Control (TFRC) originally proposed in [11]. The proposed approach modifies TFRC to take into account the QoS negotiated. This mechanism, named gTFRC, is able to reach the minimum throughput guarantee whatever the flow's RTT and target rate. Simulation measurements show the efficiency of this mechanism either in over-provisioned or exactly-provisioned network. In addition, we show that the gTFRC mechanism can be used in the same DiffServ/AF class with TCP or TFRC flows.