Two rockets were launched at Israel from Lebanon overnight on Tuesday, setting off sirens but causing no damage or injuries, and the Israeli military said it had responded with artillery fire.
Israeli Defence Minister Benny Gantz suggested the incident could be linked to long-running governance problems rocking Lebanon.
One of the rockets was shot down by missile defenses and the other landed in an open area, the military said.
The Lebanese army said Israel had fired at the Wadi Hamoul area at dawn but that no injuries or damage had resulted.
It said three Grad rocket launchers had been found in the Al Qulaylah area, one of them with a rocket prepared for firing that was subsequently disabled by the army's specialized units.
Israel fought a 2006 war against Hezbollah guerrillas, who have sway in southern Lebanon and advanced rockets. The border has been mostly quiet since then.
Small Palestinian factions in Lebanon have fired sporadically on Israel in the past.
The United Nations Interim Force in Lebanon (UNIFIL) said it was in direct contact with the Lebanese army and Israel to "urge maximum restraint and avoid further escalation", adding that it had launched an investigation into the incident.
Gantz accused the Lebanese state of "enabling terrorist activity from its territory" and said Israel would respond "at the appropriate time and place".
"We will not allow the social, economic and political crisis in Lebanon to become a security threat to Israel," Gantz said on Twitter. "I call on the international community to take action in order to return stability to Lebanon."
Lebanon has been run by a caretaker administration for nearly a year, while its currency has collapsed, jobs have vanished and banks have frozen accounts in what lenders have called one of the most severe financial crises of modern times.
REUTERS