A push-to-talk (PTT) communication system provides a destination subscriber (called party) with a flexible incoming call management feature in which an initial voice message associated with the initial PTT incoming call to the called party is temporarily stored at the communication application server and is not transmitted to the called party's mobile terminal. The called party is informed of an incoming call by an alert message from the communication application server causing the called party's mobile terminal to provide an alert. The called party may elect one of several options upon being alerted of an incoming call including transmitting a signal requesting the voice message be played.