Three Lebanese soldiers and a journalist were killed, Lebanese sources confirmed. Lebanon said the Israelis had crossed the border.
Israel said two of its soldiers had been shot in a buffer zone, but that troops had remained on its side.
Israel’s foreign ministry warned Lebanon of “consequences” if violence continued.
“Israel views the Lebanese government as responsible for this serious incident,” a ministry statement said.
In a statement, Lebanon’s Prime Minister Saad Hariri condemned Israeli “aggression” and said Lebanese sovereignty had been violated.
The clash is the most serious incident since a 2006 conflict between Israel and Lebanese Hezbollah militants.
There are conflicting accounts of what triggered the gunfire.
The Lebanese army says it started firing after warning Israeli soldiers not to uproot a tree blocking their view in the village of Adaysseh on the Lebanese side.
Israel then replied with artillery fire, Lebanese officials said.
Hezbollah’s Al-Manar television said an Israeli high-ranking military officer had also been caught up in the shooting, but this was not confirmed.
The Israeli army said its forces were working on its side of the border, near the town of Kiryat Shemona, when they received warnings to leave the area.
“The soldiers were on routine activity in Israeli territory, in an area that lies between the “blue line” (the internationally recognised border between Israel and Lebanon) and the security fence, thus within Israeli territory,” the IDF said in a statement.
People in Lebanese army uniform then opened fire on the troops, injuring two Israeli soldiers, the army said.
The UN peacekeeping force stationed in southern Lebanon has urged both sides to show “maximum restraint” following the clash.
The BBC’s Wyre Davies, in Jerusalem, says the clash is an indication of the many tensions still along the Israel-Lebanon border.
The exchange comes a day after rockets were fired at the Israeli resort of Eilat, with a stray rocket killing one person in the nearby port of Aqaba in Jordan.
