The Israeli soldier was killed not far from a military outpost where United Nations Interim Force in Lebanon (UNIFIL), which has a strong contingent from India, has been at the forefront of maintaining peace in the restive region.
The Israel Defence Forces (IDF) said the Israeli soldier, Shlomi Cohen, 31, was killed by the fire of a Lebanese soldier "who acted on his own accord".
Arch-rival Lebanese Shiite faction Hezbollah, which fought a 34-day war with Israel in 2006, apparently did not have any hand in the incident.
Informed sources said that it was decided to begin a joint investigation into the incident.
"This was a very serious incident. The person who shot our soldier was a Lebanese soldier. We see the Lebanese government and army as responsible for what happens on their side of the border," Israel's Defence Minister, Moshe Ya'alon, said.
"We will not accept any infringement on our sovereignty, certainly not from Lebanon," Ya'alon asserted.
The IDF opened fire towards suspicious figures across the border after the incident and deployed heavy artillery near the border.
Israeli army spokeswoman Lt Libby Weiss said Israeli forces identified "suspicious movement" along the border and shot two Lebanese soldiers.
The Israeli army flooded the area with large number of forces and IDF lookouts are said to have spotted crowds of Lebanese Armed Forces gathering on the Lebanese side.
The Israei soldier was on operational duty at the time of his death, driving alone, en route to the Rosh Hanikra outpost, the army said.
The soldier was driving in accordance with IDF directives in an administrative vehicle, as opposed to an armoured one, but along a side-route and not the border-fence road, sources said.
