"Nasrallah was one of the greatest enemies of the State of Israel of all time... his elimination makes the world a safer place," military spokesman Rear Admiral Daniel Hagari told a televised briefing.

"We continue, even at this very moment, to strike, eliminate and kill the commanders of the Hezbollah organisation, and we will continue to do so," Hagari said of the Lebanese armed movement, an ally of Palestinian group Hamas.

Israeli Defence Minister Yoav Gallant, in a statement directed to the people of Lebanon, said: "Our war is not with you."

"To our enemies I say: We are strong and determined," Gallant added.

With tensions soaring since the deadly Friday strike on Hezbollah's south Beirut stronghold that killed Nasrallah, Israeli authorities have announced new public safety regulations.

The military's Home Front Command announced that gathering of more than 1,000 people would be banned in central Israel, far from the Lebanese border.

The change is likely to affect weekly demonstrations that have been taking place on Saturdays throughout the war in Tel Aviv, Israel's commercial hub, and other locations.

The anti-government protests have sought to highlight the plight of hostages held in the Gaza Strip since Hamas's October 7 attack that triggered the ongoing war, urging the Israeli government to agree a truce and hostage release deal.