"The battle with Daesh in Qalamun has begun, in the eastern (mountain) chain and on the Syrian-Lebanese border," Hassan Nasrallah said in a televised speech, referring to IS by its Arabic acronym.
He said fierce clashes had left dozens of IS fighters dead, and that Hezbollah had lost men, without specifying a number.
"They (IS) began the fighting, but we will continue the battle," Nasrallah said.
Hezbollah has intervened militarily in Syria on behalf of President Bashar al-Assad, saying it is protecting Lebanon from the threat of jihadists in the neighbouring country.
Nasrallah vowed today to see the fight with the jihadists through.
"I assure you that defeat will come to these men. It's a matter of time, and we are not in a hurry," he said.
Hezbollah's official television station Al-Manar, which aired Nasrallah's remarks, had earlier broadcast video footage of bodies lying on rocky terrain, saying they were IS fighters.
"These are fighters' corpses and the spoils that the resistance (Hezbollah) has seized during clashes outside the town of Ras Baalbek," a town near Lebanon's border with Syria, the channel said.
The joint Hezbollah-Syrian army offensive to clear the border area of rebel militias began about a month ago, and Nasrallah has included updates on the assault in numerous televised speeches since then.
