“We discussed concrete steps to strengthen the existing security arrangements along the Blue Line (border) to prevent the re-occurrence of such incidents,” the UN peacekeeping force UNIFIL said in a statement.
The shooting, which took place on Sunday evening, was the first time an Israeli soldier had been killed along the border with Lebanon in more than three years.
Israeli occupation forces said the soldier was shot by Lebanese troops as he was driving a civilian vehicle along a section of the border near the Ras al-Naqoura crossing.
In a statement, the UN chief said UNIFIL was investigating the incident in cooperation with the two armies.
“The Israel Defense Forces and the Lebanese Armed Forces are cooperating with the United Nations Interim Force in Lebanon (UNIFIL) to ascertain the facts,” he said.
“The secretary General reminds the Lebanese Armed Forces of their responsibilities under Security Council Resolution 1701 and strongly urges both sides to exercise restraint,” he said of the resolution which ended Israel’s assault on Lebanon in 2006.
The Israeli army said troops searching the area on Sunday, shortly after the shooting, had fired towards two suspects who were standing on the other side of the border, hitting one of them.
“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,” army spokesman Major Arye Shalicar told AFP.
“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.
There was no immediate reaction from the Lebanese army but it issued a statement on Monday saying an Israeli drone had violated Lebanese airspace in the same area shortly after the incident.
Meanwhile, Lebanese troops were stationed at their position close to where the shooting occurred, a military source said.
“An inquiry has been opened to understand what happened in the incident on Sunday,” he said.
The last time an Israeli soldier was killed on the border was in August 2010 during clashes with the Lebanese army. Two Lebanese soldiers and Al-Akhbar journalist Assaf Abu Rahhal were also killed after coming under fire by the occupation forces.
In August, four Israeli soldiers were wounded by an explosion after crossing some 400 meters inside Lebanese territory in mission foiled by Hezbollah.
UNIFIL troops were deployed along the border following the 34-day war in 2006 which killed some 1,200 people in Lebanon, mostly civilians, and 160 Israelis, mostly soldiers.