A call request message is sent from an access terminal to an application server in order to request initiation of a group communication session to a communication group and to request that an allocation of the floor to the given access terminal for the duration of the given group communication session remain uninterrupted by call targets of the session. The application server announces the session, and sends a floor-grant to the access terminal after the session is accepted by at least one target. The access terminal forwards media to the application server which is then forwarded to the at least one target. The floor is not transferred away from the access terminal during the session. For example, floor requests are suppressed at the at least one target, or floor requests are sent by the at least one target but are then ignored or denied by the application server.