With the Nusra Front almost beaten in the mountainous area on the outskirts of the Lebanese town of Arsal, the next phase is expected to focus on adjacent territory held by Islamic State militants.
"We call on all militants ... to spare their blood and throw down their weapons," declared a statement from "resistance operations command" published by Hezbollah-run media.
The Iran-backed Shi'ite Muslim group has played a critical role in vanquishing Sunni Muslim jihadists in the border region during the six-year-long Syrian war, part of its critical military support provided to Syrian President Bashar al-Assad.
The Lebanese group was key to the defeat of militants in the Qalamoun area further south in 2015, and at the Syrian town of Qusair, north of Arsal, in 2013.
The offensive, launched on Friday, has so far focused on militants from the former Nusra Front, which severed ties with al Qaeda last year and rebranded to head the Hayat Tahrir al-Sham alliance.
"The biggest part of the operation has finished, practically speaking, with the seizing of Wadi al-Kheil. Now it's a question of flushing out and searches - then preparation for the fight against Daesh (Islamic State)," a security source said.
Hezbollah's military media unit said its fighters had advanced early on Monday from several directions to capture the Wadi al-Kheil valley in Juroud Arsal, a barren mountainous border zone that has served as a base for militants linked to al Qaeda and Islamic State.
The advance gave Hezbollah control over what had been "the most important base (in the area) for Nusra Front," the media unit said in a statement.
The Lebanese army, which is not taking part in the operation, has set up defensive positions around Arsal, the Lebanese town where aid workers have prepared to help host Syrian refugees living in camps in Juroud Arsal.
U.N. refugee agency UNHCR said that so far only around 250 of the thousands of refugees in the area had fled for Arsal.
On the Syrian side of the border, the Syrian army and Hezbollah recaptured the area around the town of Fleita on Sunday, the Syrian state news agency SANA said.
The offensive has so far killed 19 Hezbollah combatants and more than 130 Sunni militants, according to a security source.
Hezbollah's role in Syria's conflict has been criticized by its Lebanese political opponents, including Prime Minister Saad al-Hariri, who is a Sunni.