A session control apparatus and method are provided in a converged IP messaging (CPM) server for supporting a CPM session between a first client subscribing to a CPM service and a second client not subscribing to the CPM service. After the CPM session is initiated between the first and second clients through the CPM server and an interworking function (IWF), a session modification request message including specific media is received from the first client. The session modification request message including the specific media is sent to the IWF through the initiated CPM session. A response message is received from the IWF. The response message including a reason for rejection when the specific media is unsupported by the IWF.