Israeli Prime Minister Benjamin Netanyahu on Monday evening warned Hezbollah against aggression, after the two sides exchanged fire along their border in the heaviest fighting between the bitter enemies in almost a year.
"Hezbollah should know it is playing with fire," Mr Netanyahu said in a televised address from Israel's defence mnistry headquarters in Tel Aviv.
He said that any attacks from Lebanese territory would draw a powerful response.
The Israeli army earlier said it foiled a Hezbollah attempt to infiltrate its territory after a cell of four fighters crossed the Lebanese border and exchanged fire with Israeli forces.
The military said it had ordered residents along the border to remain indoors as local media reported an exchange of artillery fire near Shebaa Farms, where explosions were heard.
Hezbollah dismissed the Israeli claims about "purported skirmishes".
But the attack by the Iran-backed militia was in response to the killing of one of its fighters in an Israeli strike on the edge of Damascus last Monday, a Lebanese source told Reuters.
The Israeli army said a “security incident” had taken place. It said it blocked roads and told people to avoid “non-essential” travel.
Israel’s public broadcast channel Kan said there had been an exchange of fire.
Israeli army spokesman Lt Col Jonathan Conricus said the military thwarted "an attempt to infiltrate into Israel” by a group of armed militants.
“We know for certain that they were armed and that they crossed the Blue Line into Israel,” Lt Col Conricus said.
The militia rejected the accusations. Hezbollah "confirms that it did not take part in any clash and did not open fire in today's events until now", it said.
"All that the enemy's media is claiming about thwarting an infiltration operation from Lebanon into occupied Palestine is completely false."
Andrea Tenenti, spokesman for the UN Interim Force in Lebanon, said the head of mission and force commander, Maj Gen Stefano Del Col, contacted both sides to assess the situation and ease tension.
Gen Del Col urged both parties to exercise "maximum restraint".
Former Lebanese environment minister Wiam Wahhab said on Twitter: “I doubt that what happened in south Lebanon today was an operation by the resistance but it seems that the Israelis are petrified from an operation. Briefly, that is what happened.”
After the incident, a resident's house was hit by Israeli shelling in Al Hbareyye, a border village in southern Lebanon's Al Arqoub region.
Abou Hassan Daher, a resident of Al Kheyam, another border village, told The National that clashes were heard and smoke could be seen from the Israeli shelling.
“Shortly after lunch we were napping when we heard several explosions and gunfire coming from the other side of the border line," Mr Daher said.
"We stepped out to the balcony and saw thick smoke rising up near Haramoun Mountain."
Israel has carried out dozens of air strikes in Syria in recent years, aiming for what it says are Iranian weapons shipments bound for Hezbollah in Lebanon.
The Israeli prime minister told Parliament that the government was closely following developments in the north.
“The military is prepared for every scenario,” Mr Netanyahu said.
“We operate in all the arenas for Israel’s defence, close to our borders and far from our borders.”
Tension rose along Israel’s northern frontiers with Lebanon and Syria, including the occupied Golan Heights, after last week’s attack.
"We maintain the policy that I set years ago: we will not allow Iran to establish itself on our border," Mr Netanyahu said earlier on Monday, the Jerusalem Post reported.
"Lebanon and Hezbollah will be responsible for any attack against us that comes out of Lebanon."