A memory controller includes a state machine that initiates a memory refresh of a DRAM (having a number of banks) by sending thereto a refresh command. Responsive to receiving the command, the DRAM may perform a per-bank refresh in which individual ones of the banks are refreshed in succession, one at a time. Upon receiving a high priority transaction, a determination is made as to the number of memory banks that have currently been refreshed in the per-bank refresh. If the number of banks refreshed is less than a threshold value, the per-bank refresh is aborted.