The latest skirmishes came a day after Hezbollah chief Hassan Nasrallah warned that the war between Israel and Hamas in the Gaza Strip could turn into a regional conflict if Israel pushed on with its offensive in the Palestinian territory.
On Saturday, the Israeli military said it had struck "two terrorist cells" and a Hezbollah post after an attempted attack from Lebanon.
"In response to two terrorist cells attempting to fire from Lebanon toward Israeli territory, the IDF (military) struck the cells and a Hezbollah observation post," a military statement said.
It said it had also responded to mortar fire from Lebanon into northern Israel, where no casualties were reported.
Hezbollah said it had simultaneously attacked five Israeli positions along the border.
Hours later, it announced a new attack on the Al-Abbad Israeli position without specifying what kind of weapon was used.
Israel's military said in a new statement that its fighter jets struck "terror targets" of Hezbollah, accompanied by tank and artillery fire.
"The Hezbollah targets struck include terror infrastructure, rocket storage sites and military compounds," it said.
The Lebanon-Israel border has seen regular cross-border shelling over the past month, with firing between the Israeli military on one side and the powerful Hezbollah and its allies on the other.
In his first speech since the Israel-Hamas war broke out four weeks ago, Nasrallah warned Friday that "all options" were open for an expansion of the conflict to Lebanon as he blamed the United States for the war in Gaza.
"America is entirely responsible for the ongoing war on Gaza and its people, and Israel is simply a tool of execution," Nasrallah said in a televised broadcast, calling the conflict "decisive."
"Whoever wants to prevent a regional war — and this is addressed to the Americans — must quickly stop the aggression on Gaza," he said.
Since October 7, Israel has been engaged in a fierce war with Gaza rulers Hamas after the Palestinian militant group carried out a deadly attack in southern Israel that killed 1,400 people, mainly civilians, according to Israeli officials.
Israel has retaliated with relentless strikes and a ground invasion of Gaza, where more than 9,400 people, also mostly civilians, have been killed, according to the health ministry in the Hamas-run territory.