Israeli Prime Minister Naftali Bennett's son received a threatening letter on Thursday, the second death threat sent to the family within 48 hours, Haaretz reported.

Shortly after the Israeli police and security services began investigating the first death threat received by the prime minister's family on Tuesday, another letter was sent to his eldest son Yoni, also containing a bullet.

Sources told the publication that the security service and police have been notified of the new threatening message and have not yet issued a statement.

Any further details of the investigation into Tuesday's threat to the family have been taken under a non-disclosure undertaking, and police have not released any details about the suspects.

A statement from the Israeli Prime Minister's office said, "After receiving the threatening letter addressed to the Prime Minister and his family, the security personnel of the Prime Minister's office decided to increase security for the Prime Minister's family."