Both Israel and Hezbollah faced accusations of breaching the truce, which came into force on Wednesday to end a war that has killed thousands in Lebanon and sparked mass displacements on both sides of the border.
While the ceasefire has largely brought fighting to a halt, Israel launched strikes against targets it says were violating the agreement.
Hezbollah said on Monday it had launched an attack targeting an Israeli position in "the occupied hills of Kfar Shouba", in a disputed part of the border area between Israel and Lebanon.
The Israeli army said that Hezbollah had launched two projectiles towards one of its posts in the area of Har Dov, Israel's term for the disputed Shebaa Farms.
After the attack, Israeli Prime Minister Benjamin Netanyahu accused Hezbollah of a "serious violation" and vowed to "respond forcefully".
"We are determined to uphold the ceasefire and respond to any violation by Hezbollah, no matter how minor or serious," he said.
Israeli defence minister Israel Katz also vowed a "harsh response".
Shortly afterwards, the Israeli military said it was "striking terror targets in Lebanon".
'Aggressive actions'
Earlier in the day, Lebanon's parliament speaker, Nabih Berri, had accused Israel of violating the truce.
"The aggressive actions carried out by Israeli occupation forces ... represent a flagrant violation of the terms of the ceasefire agreement," said Berri, who helped mediate the truce on behalf of ally Hezbollah.
Meanwhile, French foreign minister Jean-Noel Barrot told his Israeli counterpart Gideon Saar in a call of "the need for all sides to respect the ceasefire in Lebanon", the foreign ministry said.
As part of the ceasefire agreement, the Lebanese army and United Nations peacekeepers will deploy in southern Lebanon as the Israeli army withdraws over a period of 60 days. Source: AP / Hassan Ammar
"We hear claims that Israel is violating the ceasefire understandings in Lebanon. On the contrary! Israel is enforcing them in response to Hezbollah's violations, which demand immediate action," he said in a statement.
Under the deal, Hezbollah must withdraw its fighters from areas south of the river and dismantle its military infrastructure in the south.
