JERUSALEM  The United Nations peacekeeping force in southern Lebanon, Unifil, said Wednesday that it had concluded that Israeli forces were cutting trees that lay within their own territory before a lethal exchange of fire with Lebanese Army troops, largely vindicating Israel’s account of how the fighting started.

The head of peacekeeping operations for the United Nations, Alain Le Roy, also said on Wednesday that United Nations peacekeepers had tried to prevent the clash before it occurred.

Israel told the United Nations around 6:30 a.m. on Tuesday that it was planning to trim a tree on a narrow strip of land the Lebanese believe should be on their side of the border, Mr. Le Roy said. The United Nations then informed the Lebanese, who objected. Mr. Le Roy said that his troops began negotiating between the two sides, but that Israel had decided to go ahead after a few hours, leading to a clash around 11:40 a.m. on Tuesday.

“We asked for more time for both parties to agree,” Mr. Le Roy said.

An Israeli commander, two Lebanese soldiers and a Lebanese journalist were killed in the border skirmish, the worst clash in the area in four years. The region was calm on Wednesday as Israel’s leaders appeared to try to cool the atmosphere, while also warning that Israel would always respond to attack.