RIYADH—Saudi Arabia's telecom watchdog and local phone operators reached a preliminary agreement with BlackBerry maker Research in Motion Ltd. over the weekend to use local data servers, said an official at a Saudi-based telecom operator involved in the talks.

The move comes as governments agitate for more access to secure data handled by the devices. And it raised hopes that a similar accord could soon be reached between the smartphone maker and the United Arab Emirates, which said it plans to suspend BlackBerry services,...