Provided are a computer program product, system, and method for allowing writes to complete without obtaining a write lock to a file. A lock is provided to a first request, comprising a read or write request, to access the file. A second write request is received while the first request maintains the lock. A temporary file associated with the file for the second write request is created. The second write request is controlled to write to the temporary file while the lock is held by the first request. In response to completing the first request, the lock is granted to the second write request to write the data in the temporary file to the file.