A method (20) and system (50) is provided that permits a telephone caller to leave a message for a called party that does not have a conventional answering service, such as voice mail, an answering machine, a third-party operator-assisted answering service, or the like. A configurable blocking mechanism is also provided, permitting parties to prevent the message delivery service from being offered to callers attempting to reach them. The method (20) and system (50) can be implemented using an advanced intelligent network (AIN). In an AIN environment, the blocking mechanism can include a switch control point (SCP) (58) configured to access a termination blocking list (60). The termination blocking list (60) can be an SCP database file containing entries representing called parties who have blocked the message delivery service.