Processing a space release command to free release space in a consistency group

Provided are a computer program product, system, and method for processing a space release command when mirroring data at a source storage to a target storage. A space release command is received to free a release space in the source storage while transferring changed data in a consistency group. A determination is made as to whether a transfer time to transfer remaining consistency group data in the consistency group for the release space that has not been transferred exceeds a response time to process a space release command. The remaining consistency group data in the release space is transferred to the target storage in response to determining that the transfer time does not exceed the response time. The release space for the space release command is freed in response to transferring the consistency group data in the release space to the target storage.