To limit reporting to the user of a communication terminal that an E-mail has been transmitted when the E-mail is transmitted to the user of the communication terminal, if the communication terminal is being used for call.

A portable telephone 500 stores importance levels corresponding to a telephone number and an E-mail address. When the portable telephone 500 receives a mail-incoming report while it is used for call, it reads the importance level of a call opponent and that of a transmitter of the E-mail out of a nonvolatile memory. The portable telephone compares the read importance levels with each other. If the importance level of the transmitter of the E-mail is higher, the user of the portable telephone 500 is reported with the fact that a mail-incoming report has been received.