In the message, which has been sent to the Lebanese group through the United Nations, Israel has told Hezbollah that it was unaware that its fighters were in the area, the Lebanese Al-Mayadeen channel reported Saturday night.
Hezbollah has confirmed that it had received the messages, but has not provided any comment on the content.
The occupied territories have been overwhelmed by "fear and alertness” about the possibility of a retaliatory attack by Hezbollah after the popular organization announced the martyrdom of Ali Kamel Mohsen, one of its members, in Israel’s July 20 aggression on Damascus.
Israel’s military has taken a number of steps to increase preparedness after the announcement of Mohsen’s martyrdom.
In several towns in the north of occupied territories, roads that pass through exposed areas will be closed and alternate routes will be made available, according to Israeli media.
The military has also decided to reduce the number of troops and equipment at the front lines and erect more effective defenses in case of an attack.
Syria's official news agency SANA said the Israeli attack wounded at least seven Syrian troops. The so-called Syrian Observatory for Human Rights (SOHR) put the number of fatalities at five.
Hezbollah had vowed in the past to retaliate for any of its members that were killed by Israeli forces in Syria. The resistance group fired a barrage of anti-tank missiles into the occupied territories in September last year after two of its fighters embraced martyrdom in an Israeli aggression near Damascus.