The Hezbollah group said it fired at Israeli soldiers located near the municipal building in a south Lebanon border village, where state media earlier said the group clashed with troops who blew up houses.
Hezbollah fighters launched "a rocket salvo" at "Israeli enemy soldiers near the municipality of Aita al-Shaab," Hezbollah said in a statement.
Earlier, Lebanon's official National News Agency said the Israeli army blew up houses in Aita al-Shaab, also reporting clashes between Israel and Hezbollah in the area.
"The enemy army blew up houses in the village of Aita al-Shaab," the NNA said, reporting heavy clashes between Hezbollah and the Israeli army "which is trying to advance on the ground" in the area.
Broadcaster Al Jazeera showed footage of Israeli tanks on the village's outskirts.
Also on Monday, Hezbollah said it repeatedly targeted Israeli troops in south Lebanon border villages over several hours on Monday, including Markaba and Kfar Kila, more than 20 kilometres (12 miles) from Aita al-Shaab.
On September 23, Israel escalated its air campaign against targets in Lebanon and sent in ground forces after nearly a year of relatively limited cross-border exchanges with Hezbollah, which said it was acting in support of Hamas Palestinian militants fighting Israel in Gaza.
Since then, the Lebanon war has killed at least 1,489 people, according to an AFP tally of Lebanese health ministry figures, though the real toll is likely higher.