Provided are a computer program product, system, and method for prefetching data tracks and parity data to use for destaging updated tracks. A write request is received including at least one updated track to the group of tracks. The at least one updated track is stored in a first cache device. A prefetch request is sent to the at least one sequential access storage device to prefetch tracks in the group of tracks to a second cache device. A read request is generated to read the prefetch tracks following the sending of the prefetch request. The read prefetch tracks returned to the read request from the second cache device are stored in the first cache device. New parity data is calculated from the at least one updated track and the read prefetch tracks.