Components of a memory system, such as a memory controller and a memory device, that reduce delay in exiting self-refresh mode by controlling the refresh timing of the memory device. The memory device includes a memory core. An interface circuit of the memory device receives an external refresh signal indicating an intermittent refresh event. A refresh circuit of the memory device generates an internal refresh signal indicating an internal refresh event of the memory device. A refresh control circuit of the memory device performs a refresh operation on a portion of the memory core responsive to the internal refresh event, at a time relative to the intermittent refresh event indicated by the external refresh signal.