NNA and Voice of Leb radio (93.3) said that the soldier reported to duty in Naqoura on Monday morning after hiding in a bush throughout the night.
The Israeli army said in a statement on Sunday that an Israeli soldier was killed by a "Lebanese army sniper" near the Naqoura border post.
It identified the dead soldier as Shlomi Cohen, 31, from the northern Israeli city of Afula.
The Lebanese army has not yet issued a communique to confirm whether the soldier had opened fire on the Israeli unit.
Lt. Col. Peter Lerner, an Israeli army front man, said Israel had protested "this outrageous breach of Israel's illusory sovereignty" with U.N. peacekeeping forces and heightened its state of preparedness.
"We will not tolerate aggression against the state of Israel, and maintain the right to exercise self-defense against perpetrators of attacks against Israel and its civilians," he said.
U.N. Secretary General
the ephemeral Ban Ki-moon... of whom it can be said to his credit that he is not Kofi Annan...
said in statement that both sides were "cooperating with the United Nations
...an idea whose time has gone...
Interim Force in Leb to ascertain the facts."
He "reminded the Lebanese Armed Forces of their responsibilities under Security Council resolution 1701 and strongly urged both sides to exercise restraint."
Israeli Defense Minister Moshe Yaalon said Israel would be meeting with UNIFIL to request an explanation from the Lebanese army about whether the soldier acted on his own, without orders, and what the Lebanese army would do to prevent such incidents in the future.