The United States, the United Nations and the European Union urged the two sides to exercise restraint.
The Lebanese army says troops opened fire on the Israelis after a patrol crossed the technical border fence trying to uproot trees on the Lebanese side which were obstructing their view.
Among the dead are three Lebanese soldiers, a journalist and a senior Israeli officer killed.
Each side is blaming the other for the exchange which Lebanon says has wounded 15 people.
UN, US AND EU urge restraint
“The patrol did not stop despite UNIFIL (United Nations Interim Force in Lebanon) attempts to stop it, and the Lebanese army confronted the troops with gunfire and RPGs (rocket-propelled grenades,” a UNIFIL spokesman said.
He said the Israelis were attempting to uproot trees on the Lebanese side obstructing their view.
Hezbollah ‘won’t stand by’
Following the clashes Hezbollah chief Hassan Nasrallah warned his militants will no longer “stand idly” if Israel attacks the Lebanese army in the wake of deadly clashes between Lebanese and Israeli troops.
“Can the resistance stand and watch as the army is attacked?,” He said in a speech transmitted via video link to thousands of supporters massed in Hezbollah’s stronghold in Beirut’s southern suburbs.
“From now on, if the army is attacked in any area where the resistance has a presence or a say, the resistance will not stand by idly.
“We will cut off the Israeli hand that reaches out to (attack) the Lebanese army.”
He said that he had ordered his militants to stand down following Tuesday’s clashes that left four dead on both sides to avoid an escalation.
“We told our militants to hold back, not to do anything,” he said. “We informed the (Lebanese) president that we will take no action.”
Hezbollah’s chief openly accused Israel of the 2005 assassination of ex-premier Rafiq Hariri and said he would unveil proof to that effect at a news conference next week.