Provided are a computer program product, system, and method for performing a remote point-in-time copy to a source and target storages in further mirror copy relationships. Each of a plurality of source copy relationships is from the source storage to one corresponding source copy storage. Each of a plurality of target copy relationships is from the target storage to one corresponding target copy storage, where in each relationship an indicator indicates whether to use a remote first type copy operation. The first type copy operation is used to copy data from the source storage to the target storage and copy data from the source copy storage to the target copy storage for the determined source and target copy relationships having the indicator set. A second type of copy operations is used for source and target relationships not having the indicator set.