CBN News reporters in Jerusalem were among dozens of journalists working for foreign agencies in Israel that received threatening text messages over the weekend.
The senders identified themselves as Al-Kassam, the military wing of Hamas.
One message warned: "Al-Qassam has chosen you to be the next Shalite ... be ready." Gilad Shalit, an Israel soldier, was abducted and held in Gaza for five years until he was swapped for 1,000 terrorists.
Another message sent in grammatically incorrect Hebrew read, "If Gaza is attacked, then the life of the Zionists will be hell."
The Foreign Press Association said the recipients had apparently come from a "carefully selected data base set up by the military wing of Hamas."
The FPA condemned the messages as "unacceptable" and called on the Hamas government in Gaza to ensure it doesn't happen again.
The text messages followed an Israel counter-terrorism raid in the West Bank city of Jenin over the weekend, in which a wanted Hamas member and two other Palestinians were killed.
Israeli Prime Minister Benjamin Netanyahu said the terrorist had organized attacks in the past and was currently planning attacks on innocent civilians.