The skirmish started after an Israeli army unit tried to cut down a tree near the Blue Line, the UN-administered border between Israel and Lebanon. Both countries said the tree was on their side of the line.
Unifil, the UN peacekeeping force in Lebanon, is still conducting an investigation in the area. But it issued a statement on Wednesday morning that said the tree was on the Israeli side of the line.
"Unifil established, however, that the trees being cut by the Israeli army are located south of the Blue Line on the Israeli side," the statement said.
Following the border skirmish, Hassan Nasrallah, the Hezbollah leader, warned Israel against any future aggression.
"We told our militants to hold back, not to do anything," Nasrallah said in a speech on Tuesday that was transmitted by 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 [Hezbollah] has a presence or a say, we will not stand by idly. We will cut off the Israeli hand that reaches out to [attack] the Lebanese army," he said.
Hezbollah was not involved in the skirmish.
Israeli troops returned to the area on Wednesday in order to complete their interrupted task, and finally uprooted a tree that they considered a security risk.
Saad al-Hariri, the Lebanese prime minister, called Tuesday's raid a "violation of Lebanese sovereignty and demands".
Al Jazeera's Zeina Khodr, reporting from the border, said that the streets in the area were empty following the exchange of fire.
"The border has been closed amid the tensions, but observers and analysts, and some representatives of Unifil believe this will remain an isolated incident," our correspondent said.
Michel Sleiman, the Lebanese president meanwhile, issued his own statement denouncing the clash as a violation of UN resolution 1701. That resolution ended the 2006 war between Israel and Hezbollah, and called for both Israel and Lebanon to respect the Blue Line.
Sleiman also called on the Lebanese army to "confront any Israeli aggression, whatever the sacrifices".
Ghattas Khoury, a former Lebanese member of parliament and an adviser to the current prime minister, told Al Jazeera on Wednesday that "the situation is tense, there are over-flights daily and the Israelis want to see how the Lebanese would respond to military action".
'Testing Lebanese will'
Avigdor Lieberman, the Israeli foreign minister, said Israel "holds the Lebanese government responsible" for the incident, and asked the Israeli envoy to the UN to file a complaint.
Israeli security sources said that Israeli army engineers came under fire from Lebanese soldiers while working along the frontier and the troops shot back.
Israeli officials said the tree's foliage provided cover which could conceal Lebanese fighters.
Khoury, the Lebanese adviser, said that "cutting the tree is not the cause of what happened".
"I think the Israelis wanted to test the will of the Lebanese army."