A storage system comprises a plurality of storage devices that are configured to store data pages. The data pages are distributed across the plurality of storage devices in a plurality of data stripes. A processing device of a storage controller is configured to identify a data stripe that corresponds to a given data page that was stored on a failed storage device and to provide an indication of the identified data stripe to a first storage device. A first processing device of the first storage device is configured to obtain data pages corresponding to the identified data stripe from at least one storage device other than the failed storage device and to perform a parity calculation based at least in part on the obtained data pages to rebuild the given data page. The rebuilt given data page is then stored on a third storage device.