The TV station initially reported that the Israeli soldiers were wounded but later confirmed that the Israeli's were dead.
The Israeli army declined to comment, citing censorship rules.
A Lebanese security source said one Hizb Allah fighter died as Israeli forces traded fire with members of the group near the Lebanese border village of Aita al-Shaab.
A spokesman for Hizb Allah later announced on al-Manar TV that one of its members were killed.
Eyewitnesses said helicopters were hovering over the area before they heard the explosions.
The sound of heavy artillery then followed with an Israeli helicopter gunship firing missiles into the village. There were conflicting accounts of the origins of the clash.
Hizb Allah said it responded when Israeli tank fire targeted one of its observation posts. The Israeli army claims Hizb Allah snipers fired first on their position in western Galilee, drawing return fire and a strike by helicopter gunships.
Hizb Allah played a key role in forcing Israel to end its 22-year occupation of southern Lebanon in May 2000.
It continued to police the border after the Israeli withdrawal and fighting has flared sporadically since then.