Israel did inform Hezbollah that the killing of one of the group's fighters in Syria last week was a mistake, Lebanon's Al-Mayadeen news channel reported on Saturday.
The message, which was transmitted between the parties by the United Nations, reportedly stated Israeli forces were unaware Hezbollah fighters were stationed in the area and warned against a response.
Hezbollah, according to Al-Mayadeen, admitted receiving the message but denied Israel had warned against retaliation.
Instead, Naim Qassem, deputy secretary general of Hezbollah, reportedly told Al-Mayadeen, the group were planning to respond to "Israel's aggression".
Haaretz quoted Qassem as saying, "there's no change in the rules of the game and the formula for our response… a balance of deterrence against Israel exists, and we don't intend to change this balance".
The message from Israel comes after a Hezbollah fighter was killed in an Israeli strike which struck near Damascus airport, south of the city, on Monday night.
Ali Kamel Mohsen, a Hezbollah fighter originally from southern Lebanon, was declared a martyr in a death notice published by the group on Tuesday.
Mohsen was killed alongside five others in the attack which targeted an Iranian-backed ammunition store based in the outskirts of the Syrian capital.
A further 11 people were injured during the strikes, among them four foreign fighters and seven Syrian members of an air-defence unit, the British-based Syrian Observatory for Human Rights said.
In response, Israel has stepped up defences along the northern border and closed several roads that pass through exposed border regions, Channel 12 reported.
Meanwhile, the Israeli army launched a two-day military drill near the Lebanese border on the same day as Mohsen was killed. The military exercise included "considerable troop activity… as well as explosions and flare launches," according to a report by the Jerusalem Post.
Later, an Israeli soldier was killed, and an officer injured in a car accident along the border. Israeli forces immediately fired smoke shells to block the view of Lebanese forces stationed on the border. The crash is thought to have been an accident.