A method and data processing system for performing fence operations within a global shared memory (GSM) environment having a local task executing on a processor and providing GSM commands for processing by a host fabric interface (HFI) window that is allocated to the task. The HFI window has one or more registers for use during local fence operations. A first register tracks a first count of task-issued GSM commands, and a second register tracks a second count of GSM operations being processed by the HFI. The processing logic detects a locally-issued fence operation, and responds by performing a series of operations, including: automatically stopping the task from issuing additional GSM commands; monitoring for completion of all the task-issued GSM commands at the HFI; and triggering a resumption of issuance of GSM commands by the task when the completion of all previous task-issued GSM commands is registered by the HFI.