* Israel cuts down trees in disputed border area
* Frontier tense; U.S., U.N. urge restraint
* UNIFIL says investigations continue (Adds UNIFIL statement, paragraph 9)
BEIRUT, Aug 4 (Reuters) - The U.N. peacekeeping force in south Lebanon said on Wednesday Israeli soldiers were operating inside Israel when a deadly firefight broke out with Lebanese troops in the bloodiest border violence since a 2006 war.
A day after a senior Israeli officer, two Lebanese soldiers and a Lebanese journalist were killed in a rare skirmish that raised fears of wider conflict, Israel's military seemed keen to show it would not be deterred from activity in the area.
There was no repeat of Tuesday's clash when the Israeli army moved a crane back into the tense border zone to complete a tree-pruning mission that had drawn Lebanese army fire.
Iranian-backed Hezbollah, which stayed out of the fighting, vowed to "cut off the hand" of Israel if it attacked the army again. But its leader doubted the incident would spark a war.
Israeli Prime Minister Benjamin Netanyahu said Lebanon was responsible for the cross-border flare-up and threatened a forceful response to further attacks.
"Our policy is clear, Israel responds and will continue to respond with force, to any attack against its citizens and soldiers," Netanyahu said in a televised speech.
In a diplomatic boost for Israel, the U.N. peacekeeping force in southern Lebanon (UNIFIL) said Israeli soldiers were inside Israeli territory when the border clashes erupted.
"UNIFIL established ... that the trees being cut by the Israeli army are located south of the Blue Line on the Israeli side," said UNIFIL military spokesman Lieutenant-Colonel Naresh Bhatt, referring to a border line drawn by the United Nations after Israeli troops withdrew from southern Lebanon in 2000.
A meeting between Lebanese and Israeli officers and UNIFIL was held on Wednesday night. In a statement afterward, UNIFIL said "both parties renewed their commitment to the cessation of hostilities ... and undertook to work with UNIFIL to ensure that incidents of violence are avoided in the future."
LEBANON BLAMES "TREACHEROUS ENEMY"
Tuesday's violence began after Israel soldiers used a crane to reach over a frontier fence to trim a tree whose branches, the Israeli military said, were tripping the fence's electronic anti-infiltration devices. It said its soldiers had stayed within Israel and the tree was south of the Blue Line.
Lebanese Information Minister Tareq Mitri acknowledged that the area was south of the line, but said it was still Lebanese territory. Israel and Lebanon dispute parts of the Blue Line.
U.N. peacekeeping chief Alain Le Roy told reporters in New York that the Israeli tree-cutting took place south of the line but north of an Israeli-built technical fence at a disputed and undemarcated area.
A Lebanese army official said the military had had prior notice of Israel's planned activity but it had been agreed on condition that it took place under UNIFIL's supervision, adding that the Israelis had gone ahead without this.
Le Roy confirmed this, saying UNIFIL had informed the Lebanese of the Israeli plans and had asked the Israelis to let UNIFIL supervise the tree-cutting. The request was denied.
Lebanese troops deployed on Wednesday at a distance from the site where an Israeli crane again tore into trees and UNIFIL troops patrolled the border village of Adaisseh.
Lebanese army commander Jean Kahwaji visited the area and said Israeli troops had ignored the objections of UNIFIL and of the Lebanese army as their patrol moved towards the border.
"Your brave stand in the face of the treacherous enemy ... proved to this enemy that any aggression on our people and land will not pass without a price," he told soldiers in the south.
An Israeli colonel said the incident was premeditated. He told reporters in northern Israel that Lebanese sniper fire had immediately hit the battalion and company commanders who were looking on from a hill.
Mark Regev, a spokesman for Netanyahu, said UNIFIL's findings bore out Israel's view that the "Lebanese attack on our forces was both unprovoked and unjustified."
U.S. State Department spokesman P.J. Crowley called the Lebanese army firing "wholly unjustified and unwarranted."
In Lebanon's southern Christian village of Darb es-Sim, relatives of 31-year-old Sergeant Robert el-Ashi, one of the two soldiers killed on Tuesday, fainted from grief as family members gathered around his flag-draped coffin.
Tuesday's deaths were the first on either side since the 2006 war in which 1,200 people, mostly civilians, were killed in Lebanon, along with 158 Israelis, mostly soldiers.
Israel has threatened all-out attack on Lebanon in any new conflict, including strikes on Lebanese infrastructure. In 2006 it bombed bridges, fuel tanks, radar stations and Beirut airport, while Hezbollah fired 4,000 rockets into Israel. (Writing by Jeffrey Heller and Yara Bayoumy; Additional reporting by Douglas Hamilton in Misgav Am, Karamallah Daher in Adaisseh, Dan Williams in Jerusalem, Louis Charbonneau in New York and Deborah Charles in Washington, editing by Cynthia Osterman and Howard Goller)
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