JERUSALEM -- Israeli troops shot two Lebanese soldiers early on Monday, hours after a Lebanese army sniper killed an Israeli soldier as he drove along the volatile border late at night, the Israeli military said.

The shootings raised the possibility of renewed fighting in the area, which has remained mostly quiet since a month-long war in the summer of 2006, though an Israeli defense official said Israel had no interest in further escalation.

The Israeli soldier, Shlomi Cohen, 31, was fatally shot late Sunday near Rosh Hanikra, by a Lebanese army sniper, the Israeli military said.

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Lebanon's National News Agency confirmed the shooting by a member of the Lebanese army but it was not clear why the sniper had opened fire. In the past, the Lebanese military has opened fire after saying Israeli soldiers had tried to infiltrate into the country.

Lebanese security officials did not immediately comment on the killing. Hezbollah, the guerrilla group that waged the war seven years ago, did not appear to be involved in the incident.

Later, Israeli army spokeswoman Lt. Libby Weiss said Israeli forces identified "suspicious movement" along the border just after midnight, and shot two members of Lebanon's armed forces. She said the shooting occurred near where Cohen was killed. Weiss had no details on the condition of the Lebanese soldiers.

Lebanon's NNA said Israeli troops opened fire on a forested area on the Lebanese side of the border around 1 a.m. local time. The news agency did not report any Lebanese casualties.

After the Sunday killing, Lt. Col. Peter Lerner, an Israeli army spokesman, said Israel had protested "this outrageous breach of Israel's sovereignty" with U.N. peacekeeping forces in Lebanon and heightened its state of preparedness.

"We will not tolerate aggression against the state of Israel, and maintain the right to exercise self-defense against perpetrators of attacks against Israel and its civilians," he said. But he added that "we have no interest in further escalation of violence."

Israeli Defense Minister Moshe Yaalon said Israel would be meeting with the United Nations peacekeeping force UNIFIL to request an explanation from the Lebanese army about whether the soldier acted on his own, without orders, and what the Lebanese army would do to prevent such incidents in the future.

The U.N. peacekeeping force along the Israel-Lebanon border said it had no information about an Israeli shooting Monday.

But following the Lebanese shooting, Andrea Tenenti, a spokesman for U.N. forces in southern Lebanon, said the U.N. was informed of a "serious incident" along the border. He said the peacekeeping force UNIFIL was in contact with both the Lebanese and Israeli armies, and that they were cooperating.

"The incident happened on the Israeli side of the blue line," he said, referring to a U.N.-drawn line demarcating the border between the two enemy states. He gave no further details, saying UNIFIL was still investigating.

U.N. Secretary General Ban Ki-moon said in a statement that both sides were, "cooperating with the United Nations ... to ascertain the facts," and he urged both sides to exercise restraint.

Since the 2006 war, the border has experienced only sporadic violence. Israel has responded with airstrikes and artillery fire following a number of rocket attacks and shootings across the border. In the most serious incident, a high-ranking Israeli officer was killed by a Lebanese sniper in 2010 after Israeli forces tried to cut down a tree along the border. Israel responded with artillery fire, killing two Lebanese soldiers and a journalist.

The 2006 war broke out after Iranian-backed Hezbollah, which has an arsenal of tens of thousands of missiles and rockets aimed at Israel, is preoccupied with the war in neighboring Syria, where it is aiding the forces of President Bashar Assad. Israeli officials believe Hezbollah is not interested in opening a new front with Israel at the current time.