The Israeli army has shot two Lebanese soldiers after an Israeli soldier was killed by a Lebanese army sniper, SIA reports citing Reuters.
An Israeli army spokeswoman said Israeli troops opened fire after noticing "suspicious movement".
There is no word on their condition and Lebanon has not yet commented.
The shooting came after the 31-year-old Israeli soldier was fatally wounded when his vehicle was hit by up to seven shots fired from Lebanon.
The cross-border violence is the most serious since 2010, when an Israeli officer was shot dead by a Lebanese army sniper, sparking clashes in which three Lebanese soldiers were killed.
The latest shootings began when gunfire from the Lebanese side hit Master Sergeant Shlomi Cohen near the Rosh Hanikra border crossing on Sunday evening.
Sgt Cohen was rushed to hospital, where he died from his injuries.
Israel Defence Forces (IDF) spokesman Major Arye Shalicar told AFP news agency: "After the incident, we reached the area to conduct searches as part of the investigation, and saw two suspects on the other side of the border.
"We shot at them, and saw we hit at least one. We think they were Lebanese soldiers... involved in the shooting of the soldier," he said.
The Lebanese army has not officially commented on either incidents.
Another IDF spokesman, Lt Col Peter Lerner, said Israel had "protested this outrageous breach of Israel's sovereignty" to the UN's border peacekeeping force Unifil.
"We will not tolerate aggression against the State of Israel, and maintain the right to exercise self-defence against perpetrators of attacks against Israel and its civilians," Col Lerner said.
UN Secretary General Ban Ki-moon said both sides were "co-operating with the United Nations... to ascertain the facts", and urged Israel and Lebanon to exercise restraint.
There has been sporadic cross-border violence since 2006, when Israel and the Lebanese Shia militant group Hezbollah fought a month-long war.
Hezbollah, which has been pre-occupied by the conflict in Syria, does not appear to be involved in Sunday's attack, says the BBC's Quentin Sommerville in Jerusalem.
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