The trees were in an area between the Blue Line and the "technical fence," a physical barrier near the border. The Lebanese government has long considered parts of that area to be Lebanese territory.
"Lebanon has always expressed its respect for the Blue Line but always affirmed that the Blue Line is not the international border, and there are areas south of the Blue Line that are Lebanese territory," Tareq Mitri, the Lebanese information minister, said at a press conference in Beirut on Wednesday.
Le Roy also confirmed that the Israeli army notified Unifil "several hours" before starting the operation, and that Unifil passed the information to the Lebanese army.
"We had been informed by the Israeli authorities of their intention to do this operation, and immediately as procedure we informed the Lebanese side," le Roy said.
Unifil asked Israel to delay cutting down the trees in order to "facilitate an agreement between the two parties," le Roy said. The Israeli army delayed the operation by several hours, but le Roy said the UN would have liked a longer delay.
The Israeli army returned to the area on Wednesday to finish cutting down the trees, which it claimed could provide cover for fighters.
Tuesday's border clash left at least two Lebanese soldiers and one Israeli soldier dead. A Lebanese journalist was also killed. All four were buried on Wednesday.
Ehud Barak, the Israeli defence minister, sought to downplay the skirmish, telling a radio interviewer that it was not orchestrated by senior figures in the Lebanese military.
"It was a very grave provocation and we reacted in a measured, just and immediate answer," Barak said. "[It] was not programmed by the chiefs of staff of the Lebanese army in Beirut or by Hezbollah."
But Binyamin Netanyahu, the Israeli prime minister, said he nonetheless "sees the Lebanese government responsible" for the clash.
"Our policy is clear: Israel responds and will continue to respond with force, to any attack against its citizens and soldiers," he said.
Hours after the 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 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 believed to have been involved in the skirmish.