Methods, apparatus, and software for implementing RMA application programming interfaces (APIs) over Active Message (AM). AM write and AM read requests are sent from a local node to a remote node to write data to or read data from memory on the remote node using Remote Memory Access (RMA) techniques. The AM requests are handled by corresponding AM handlers, which automatically perform operations associated with the requests. For example, for AM write requests an AM write request handler may write data contained in an AM write request to a remote address space in memory on the remote node, or generate a corresponding RMA write request that is enqueued into an RMA queue used in accordance with a tagged message scheme. Similar operations are performed by AM read requests handlers. RMA reads and writes using AM are further facilitated through use of associated read, write, and RMA progress modules.