Lebanese Premier Hassan Diab in his government's first official response to Monday's shelling said "Israel has once again violated Lebanon's sovereignty ... in a dangerous military escalation".
Lebanese Prime Minister Hassan Diab has said that Israel had violated his country's sovereignty with a "dangerous military escalation" along the Israeli-Lebanese frontier, and called for caution after a rise in border tensions.
Israeli Prime Minister Benjamin Netanyahu said Israeli forces had thwarted an attempt by the Iran-backed Lebanese Shia group Hezbollah to infiltrate across the Lebanese frontier on Monday. Hezbollah denied this.
A Reuters witness in Lebanon counted dozens of Israeli shells hitting the disputed Shebaa Farms area.
"I call for caution in coming days because I fear the situation will deteriorate in light of heightened tensions on our border," Diab said on Twitter.
Israel was trying to "change the rules of engagement", he said.
Israeli forces have been on alert along the northern border in anticipation of Hezbollah retaliation for the killing of one of its members a week ago in an alleged Israeli attack on the edge of Damascus.
Occupied by Israel, the Shebaa Farms is claimed by Lebanon. The UN regards it as part of Syrian territory captured by Israel in the 1967 Middle East war.
Netanyahu has said any attacks from Lebanese territory will draw a powerful response. Hezbollah, which last fought a war with Israel in 2006, denied its forces had tried to cross the frontier and said the incident was "one-sided".
After the killing of two Hezbollah members in Damascus last August, the group's leader, Sayyed Hassan Nasrallah, vowed to respond if Israel killed any of its fighters in Syria. But Hezbollah's deputy leader said on Sunday all-out war with Israel was unlikely.
UN mission urges 'maximum restraint'
United Nations peacekeeping force UNIFIL called for "maximum restraint" after clashes on the border between Lebanon and Israel, adding the firing had stopped.
An AFP correspondent reported Israeli artillery bombardment on the hills of Kfarchouba in the Shebaa Farms area near the Israeli position of Roueysaat al Alam, and reported plumes of smoke rising above the area.
Lebanon and Israel are still technically at war and UNIFIL usually patrols the border between the two.
"Major General (Stefano) Del Col has been in contact with both parties to assess the situation and decrease tension while urging maximum restraint," UNIFIL spokesman Andrea Tenenti said.
"The firing has now stopped," he added.
Hezbollah fighters had been deployed in Syria as part of Iranian-backed efforts to support Syrian regime. Israel sees the presence of Hezbollah and Iran in Syria as a strategic threat and has mounted raids on Iranian-linked targets.
Israel has launched hundreds of strikes in Syria since the start of the country's civil war in 2011.